Return on Capital Employed (ROCE) is a popular financial instrument and communication tool for the appraisal of companies. Often, companies management and other practitioners use untested rules and behavioural approach when investigating the key determinants of ROCE, instead of the scientific statistical paradigm. The aim of this dissertation was to identify and quantify key determinants of ROCE of individual companies listed on the Johannesburg Stock Exchange (JSE), by comparing classical multiple linear regression, principal components regression, generalized least squares regression, and robust maximum likelihood regression approaches in order to improve companies decision making. Performance indicators used to arrive at the best approach were coefficient of determination ( ), adjusted ( , and Mean Square Residual (MSE). Since the ROCE variable had positive and negative values two separate analyses were done. The classical multiple linear regression models were constructed using stepwise directed search for dependent variable log ROCE for the two data sets. Assumptions were satisfied and problem of multicollinearity was addressed. For the positive ROCE data set, the classical multiple linear regression model had a of 0.928, an of 0.927, a MSE of 0.013, and the lead key determinant was Return on Equity (ROE),with positive elasticity, followed by Debt to Equity (D/E) and Capital Employed (CE), both with negative elasticities. The model showed good validation performance. For the negative ROCE data set, the classical multiple linear regression model had a of 0.666, an of 0.652, a MSE of 0.149, and the lead key determinant was Assets per Capital Employed (APCE) with positive effect, followed by Return on Assets (ROA) and Market Capitalization (MC), both with negative effects. The model showed poor validation performance. The results indicated more and less precision than those found by previous studies. This suggested that the key determinants are also important sources of variability in ROCE of individual companies that management need to work with. To handle the problem of multicollinearity in the data, principal components were selected using Kaiser-Guttman criterion. The principal components regression model was constructed using dependent variable log ROCE for the two data sets. Assumptions were satisfied. For the positive ROCE data set, the principal components regression model had a of 0.929, an of 0.929, a MSE of 0.069, and the lead key determinant was PC4 (log ROA, log ROE, log Operating Profit Margin (OPM)) and followed by PC2 (log Earnings Yield (EY), log Price to Earnings (P/E)), both with positive effects. The model resulted in a satisfactory validation performance. For the negative ROCE data set, the principal components regression model had a of 0.544, an of 0.532, a MSE of 0.167, and the lead key determinant was PC3 (ROA, EY, APCE) and followed by PC1 (MC, CE), both with negative effects. The model indicated an accurate validation performance. The results showed that the use of principal components as independent variables did not improve classical multiple linear regression model prediction in our data. This implied that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Generalized least square regression was used to assess heteroscedasticity and dependences in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the weighted generalized least squares regression model had a of 0.920, an of 0.919, a MSE of 0.044, and the lead key determinant was ROE with positive effect, followed by D/E with negative effect, Dividend Yield (DY) with positive effect and lastly CE with negative effect. The model indicated an accurate validation performance. For the negative ROCE data set, the weighted generalized least squares regression model had a of 0.559, an of 0.548, a MSE of 57.125, and the lead key determinant was APCE and followed by ROA, both with positive effects.The model showed a weak validation performance. The results suggested that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Robust maximum likelihood regression was employed to handle the problem of contamination in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the robust maximum likelihood regression model had a of 0.998, an of 0.997, a MSE of 6.739, and the lead key determinant was ROE with positive effect, followed by DY and lastly D/E, both with negative effects. The model showed a strong validation performance. For the negative ROCE data set, the robust maximum likelihood regression model had a of 0.990, an of 0.984, a MSE of 98.883, and the lead key determinant was APCE with positive effect and followed by ROA with negative effect. The model also showed a strong validation performance. The results reflected that the key determinants are major sources of variability in ROCE of individual companies that management need to work with. Overall, the findings showed that the use of robust maximum likelihood regression provided more precise results compared to those obtained using the three competing approaches, because it is more consistent, sufficient and efficient; has a higher breakdown point and no conditions. Companies management can establish and control proper marketing strategies using the key determinants, and results of these strategies can see an improvement in ROCE. / Mathematical Sciences / M. Sc. (Statistics)

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: When estimating the covariance matrices of two or more populations, the covariance matrices are often assumed to be either equal or completely unrelated. The common principal components (CPC) model provides an alternative which is situated between these two extreme assumptions: The assumption is made that the population covariance matrices share the same set of eigenvectors, but have di erent sets of eigenvalues. An important question in the application of the CPC model is to determine whether it is appropriate for the data under consideration. Flury (1988) proposed two methods, based on likelihood estimation, to address this question. However, the assumption of multivariate normality is untenable for many real data sets, making the application of these parametric methods questionable. A number of non-parametric methods, based on bootstrap replications of eigenvectors, is proposed to select an appropriate common eigenvector model for two population covariance matrices. Using simulation experiments, it is shown that the proposed selection methods outperform the existing parametric selection methods. If appropriate, the CPC model can provide covariance matrix estimators that are less biased than when assuming equality of the covariance matrices, and of which the elements have smaller standard errors than the elements of the ordinary unbiased covariance matrix estimators. A regularised covariance matrix estimator under the CPC model is proposed, and Monte Carlo simulation results show that it provides more accurate estimates of the population covariance matrices than the competing covariance matrix estimators. Covariance matrix estimation forms an integral part of many multivariate statistical methods. Applications of the CPC model in discriminant analysis, biplots and regression analysis are investigated. It is shown that, in cases where the CPC model is appropriate, CPC discriminant analysis provides signi cantly smaller misclassi cation error rates than both ordinary quadratic discriminant analysis and linear discriminant analysis. A framework for the comparison of di erent types of biplots for data with distinct groups is developed, and CPC biplots constructed from common eigenvectors are compared to other types of principal component biplots using this framework. A subset of data from the Vermont Oxford Network (VON), of infants admitted to participating neonatal intensive care units in South Africa and Namibia during 2009, is analysed using the CPC model. It is shown that the proposed non-parametric methodology o ers an improvement over the known parametric methods in the analysis of this data set which originated from a non-normally distributed multivariate population. CPC regression is compared to principal component regression and partial least squares regression in the tting of models to predict neonatal mortality and length of stay for infants in the VON data set. The tted regression models, using readily available day-of-admission data, can be used by medical sta and hospital administrators to counsel parents and improve the allocation of medical care resources. Predicted values from these models can also be used in benchmarking exercises to assess the performance of neonatal intensive care units in the Southern African context, as part of larger quality improvement programmes. / AFRIKAANSE OPSOMMING: Wanneer die kovariansiematrikse van twee of meer populasies beraam word, word dikwels aanvaar dat die kovariansiematrikse of gelyk, of heeltemal onverwant is. Die gemeenskaplike hoofkomponente (GHK) model verskaf 'n alternatief wat tussen hierdie twee ekstreme aannames gele e is: Die aanname word gemaak dat die populasie kovariansiematrikse dieselfde versameling eievektore deel, maar verskillende versamelings eiewaardes het. 'n Belangrike vraag in die toepassing van die GHK model is om te bepaal of dit geskik is vir die data wat beskou word. Flury (1988) het twee metodes, gebaseer op aanneemlikheidsberaming, voorgestel om hierdie vraag aan te spreek. Die aanname van meerveranderlike normaliteit is egter ongeldig vir baie werklike datastelle, wat die toepassing van hierdie metodes bevraagteken. 'n Aantal nie-parametriese metodes, gebaseer op skoenlus-herhalings van eievektore, word voorgestel om 'n geskikte gemeenskaplike eievektor model te kies vir twee populasie kovariansiematrikse. Met die gebruik van simulasie eksperimente word aangetoon dat die voorgestelde seleksiemetodes beter vaar as die bestaande parametriese seleksiemetodes. Indien toepaslik, kan die GHK model kovariansiematriks beramers verskaf wat minder sydig is as wanneer aanvaar word dat die kovariansiematrikse gelyk is, en waarvan die elemente kleiner standaardfoute het as die elemente van die gewone onsydige kovariansiematriks beramers. 'n Geregulariseerde kovariansiematriks beramer onder die GHK model word voorgestel, en Monte Carlo simulasie resultate toon dat dit meer akkurate beramings van die populasie kovariansiematrikse verskaf as ander mededingende kovariansiematriks beramers. Kovariansiematriks beraming vorm 'n integrale deel van baie meerveranderlike statistiese metodes. Toepassings van die GHK model in diskriminantanalise, bi-stippings en regressie-analise word ondersoek. Daar word aangetoon dat, in gevalle waar die GHK model toepaslik is, GHK diskriminantanalise betekenisvol kleiner misklassi kasie foutkoerse lewer as beide gewone kwadratiese diskriminantanalise en line^ere diskriminantanalise. 'n Raamwerk vir die vergelyking van verskillende tipes bi-stippings vir data met verskeie groepe word ontwikkel, en word gebruik om GHK bi-stippings gekonstrueer vanaf gemeenskaplike eievektore met ander tipe hoofkomponent bi-stippings te vergelyk. 'n Deelversameling van data vanaf die Vermont Oxford Network (VON), van babas opgeneem in deelnemende neonatale intensiewe sorg eenhede in Suid-Afrika en Namibi e gedurende 2009, word met behulp van die GHK model ontleed. Daar word getoon dat die voorgestelde nie-parametriese metodiek 'n verbetering op die bekende parametriese metodes bied in die ontleding van hierdie datastel wat afkomstig is uit 'n nie-normaal verdeelde meerveranderlike populasie. GHK regressie word vergelyk met hoofkomponent regressie en parsi ele kleinste kwadrate regressie in die passing van modelle om neonatale mortaliteit en lengte van verblyf te voorspel vir babas in die VON datastel. Die gepasde regressiemodelle, wat maklik bekombare dag-van-toelating data gebruik, kan deur mediese personeel en hospitaaladministrateurs gebruik word om ouers te adviseer en die toewysing van mediese sorg hulpbronne te verbeter. Voorspelde waardes vanaf hierdie modelle kan ook gebruik word in normwaarde oefeninge om die prestasie van neonatale intensiewe sorg eenhede in die Suider-Afrikaanse konteks, as deel van groter gehalteverbeteringprogramme, te evalueer.

<p>Neregularnost prostiranja radio talasa je uobičajeni fenomen koji<br />utiče na kvalitet radio veze u okviru bežične mreže, rezultujući<br />različitim obrascima prostiranja radio talasa. Ova teza daje<br />predlog nekoliko postupaka analize prostiranja radio talasa u cilju<br />bez-senzorskog otkrivanja prisustva i kretanja ljudi unutar postojeće<br />bežične mreže. Indikator primljene snage radio signala predstavlja<br />osnovni element analize, iz kog se izdvajaju informaciono,<br />amplitudsko i frekventno obeležje. Analizom navedenih obeležja<br />moguća je realizacija robusnog postupka bez-senzorske detekcije ljudi<br />koja se može primeniti u različitim rešenjima ambijentalne<br />inteligencije, zahtevajući minimalan broj elemenata fizičke<br />arhitekture, neophodnih za uspostavljanje korisnički svesnog<br />okruženja.</p> / <p>Radio irregularity is a common and non-negligible phenomenon that impacts<br />the connectivity and interference in a wireless network, by introducing<br />disturbances in radio signal&rsquo;s propagation pattern. In order to detect a<br />possible presence of a human subject within the existing radio network<br />sensorlessly, this thesis analyze the irregularity data expressed in a form of<br />received signal strength variation. The received signal strength variation is<br />decomposed into information, amplitude and frequency characteristics. The<br />combination of these three characteristics analysis enables the definition of<br />robust and cost-effective device-free human presence detection method that<br />can be exploited for various ambient intelligence solutions, requiring the<br />minimum hardware add-ons that are necessary for the establishment of a<br />user aware environment.</p>

Cette thèse est consacrée à l'étude de la transmission des chocs réels et financiers en Europe, en traitant le canal du capital bancaire. La démarche suivie consiste à combiner des approches théoriques et empiriques de façon à mettre en évidence empiriquement l'hétérogénéité de transmission au niveau européen et l'ampleur du canal du capital bancaire. Le premier chapitre consiste à faire un tour d’horizon sur les fonds propres et la structure financière des banques, tout en analysant leur impact au niveau micro et macroéconomique. D'après l’analyse de la littérature relative à ce champ, le processus de transmission semble bien influencé par la spécificité des banques et leur niveau de fonds propres réglementaires. La contrainte exercée sur ces derniers détermine l’ampleur de la transmission des chocs. Le deuxième chapitre est consacré à l'étude des déterminants de la réaction des banques face à un choc. D'après les résultats, le niveau ex ante des fonds propres mais également les différentes composantes du capital réglementaire influencent la réaction des banques. Le troisième chapitre analyse les effets de Bâle I et II sur le mécanisme de transmission des chocs à partir d’un modèle d’équilibre général. Les résultats des simulations montrent que la prise en compte simultanée d’un canal du capital bancaire et d’un mécanisme d’accélérateur financier amplifie la propagation des chocs monétaires à travers un effet prime de liquidité. Le dernier chapitre est consacré à examiner un aspect particulier de la réglementation prudentielle : la résolution des défaillances des institutions financières. L’accent est mis sur les banques d’importance systémique. L’analyse des politiques de résolution adoptées montre que ces dernières ne permettent pas de réduire le risque moral. Aussi, pour prévenir de leur défaut, des règles de fermeture sont mises en place. À cette fin, une modélisation théorique conduit à conclure que des sanctions monétaires, couplées à une surveillance accrue peuvent limiter les incitations des banques à prendre des risques excessifs. Cette présente thèse a apporté de nouveaux résultats par rapport à la littérature et elle a montré le rôle à court et long terme des différents éléments de la structure du bilan des banques résultant de l'estimation du modèle VECM. / In this thesis, we study the transmission of real and financial shocks in Europe focusing on the bank capital channel. In our approach, we consider both theoretical and empirical issues. The ai mis to empirically emphasize the heteregeneity in the transmission of shocks at a European level and the extent of the bank capital channel. In Chapter 1, we do a survey on the structure of bank capital and balance sheet to analyse their impact at micro and macro levels. Considering the existing literature on bank capital and transmission channel, the transmission process seems to be influenced by banks’ specificities and by their level of regulatory capital. Regulatory constraint on bank capital determines the magnitude of the transmission of shocks. In Chapter 2, we study the determinants of banks’ reaction to a shock. Or results show that, the ex ante level of capital and the various components of regulatory capital significantly impact banks’ behaviour. In Chapter 3, we focus on the impact of Basel I and II regulatory frameworks on the transmission of shocks from a general equilibrium model. The simulation results point out that considering simultaneously the bank capital channel and the financial accelerator mechanism increases the propagation of monetary shocks through the liquidity premium effect. In Chapter 4, we examine a singular aspect of the prudential regulation : the resolution of failing financial institutions. We focus on the systemic importance banks. Current policy statements have not reduced moral hazard behaviour of such financial institutions. Thus, to prevent the catastrophic consequences of their failure, bankruptcy laws have been adopted. Considering a theoretical model, we conclude that monetary sanctions, strengthen by stronger monitoring pressures may limit banks’ incentives to take excessive risks. This thesis provides new results to the existing literature. It emphasizes the role of the several components of bank balance sheet structure in both short and long runs, resulting from an estimated VECM.

Return on Capital Employed (ROCE) is a popular financial instrument and communication tool for the appraisal of companies. Often, companies management and other practitioners use untested rules and behavioural approach when investigating the key determinants of ROCE, instead of the scientific statistical paradigm. The aim of this dissertation was to identify and quantify key determinants of ROCE of individual companies listed on the Johannesburg Stock Exchange (JSE), by comparing classical multiple linear regression, principal components regression, generalized least squares regression, and robust maximum likelihood regression approaches in order to improve companies decision making. Performance indicators used to arrive at the best approach were coefficient of determination ( ), adjusted ( , and Mean Square Residual (MSE). Since the ROCE variable had positive and negative values two separate analyses were done. The classical multiple linear regression models were constructed using stepwise directed search for dependent variable log ROCE for the two data sets. Assumptions were satisfied and problem of multicollinearity was addressed. For the positive ROCE data set, the classical multiple linear regression model had a of 0.928, an of 0.927, a MSE of 0.013, and the lead key determinant was Return on Equity (ROE),with positive elasticity, followed by Debt to Equity (D/E) and Capital Employed (CE), both with negative elasticities. The model showed good validation performance. For the negative ROCE data set, the classical multiple linear regression model had a of 0.666, an of 0.652, a MSE of 0.149, and the lead key determinant was Assets per Capital Employed (APCE) with positive effect, followed by Return on Assets (ROA) and Market Capitalization (MC), both with negative effects. The model showed poor validation performance. The results indicated more and less precision than those found by previous studies. This suggested that the key determinants are also important sources of variability in ROCE of individual companies that management need to work with. To handle the problem of multicollinearity in the data, principal components were selected using Kaiser-Guttman criterion. The principal components regression model was constructed using dependent variable log ROCE for the two data sets. Assumptions were satisfied. For the positive ROCE data set, the principal components regression model had a of 0.929, an of 0.929, a MSE of 0.069, and the lead key determinant was PC4 (log ROA, log ROE, log Operating Profit Margin (OPM)) and followed by PC2 (log Earnings Yield (EY), log Price to Earnings (P/E)), both with positive effects. The model resulted in a satisfactory validation performance. For the negative ROCE data set, the principal components regression model had a of 0.544, an of 0.532, a MSE of 0.167, and the lead key determinant was PC3 (ROA, EY, APCE) and followed by PC1 (MC, CE), both with negative effects. The model indicated an accurate validation performance. The results showed that the use of principal components as independent variables did not improve classical multiple linear regression model prediction in our data. This implied that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Generalized least square regression was used to assess heteroscedasticity and dependences in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the weighted generalized least squares regression model had a of 0.920, an of 0.919, a MSE of 0.044, and the lead key determinant was ROE with positive effect, followed by D/E with negative effect, Dividend Yield (DY) with positive effect and lastly CE with negative effect. The model indicated an accurate validation performance. For the negative ROCE data set, the weighted generalized least squares regression model had a of 0.559, an of 0.548, a MSE of 57.125, and the lead key determinant was APCE and followed by ROA, both with positive effects.The model showed a weak validation performance. The results suggested that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Robust maximum likelihood regression was employed to handle the problem of contamination in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the robust maximum likelihood regression model had a of 0.998, an of 0.997, a MSE of 6.739, and the lead key determinant was ROE with positive effect, followed by DY and lastly D/E, both with negative effects. The model showed a strong validation performance. For the negative ROCE data set, the robust maximum likelihood regression model had a of 0.990, an of 0.984, a MSE of 98.883, and the lead key determinant was APCE with positive effect and followed by ROA with negative effect. The model also showed a strong validation performance. The results reflected that the key determinants are major sources of variability in ROCE of individual companies that management need to work with. Overall, the findings showed that the use of robust maximum likelihood regression provided more precise results compared to those obtained using the three competing approaches, because it is more consistent, sufficient and efficient; has a higher breakdown point and no conditions. Companies management can establish and control proper marketing strategies using the key determinants, and results of these strategies can see an improvement in ROCE. / Mathematical Sciences / M. Sc. (Statistics)

A qualidade microbiológica de medicamentos é fundamental para garantir sua eficácia e segurança. Os métodos convencionais para identificação microbiana em produtos não estéreis são amplamente utilizados, entretanto são demorados e trabalhosos. O objetivo deste trabalho é desenvolver método microbiológico rápido (MMR) para a identificação de contaminantes em produtos farmacêuticos utilizando a espectrofotometria de infravermelho com transformada de Fourier com reflectância total atenuada (FTIR-ATR). Análise de componentes principais (PCA) e análise de discriminantes (LDA) foram utilizadas para obter um modelo de predição com a capacidade de diferenciar o crescimento de oriundo de contaminação por Bacillus subtilis (ATCC 6633), Candida albicans (ATCC 10231), Enterococcus faecium (ATCC 8459), Escherichia coli (ATCC 8739), Micrococcus luteus (ATCC 10240), Pseudomonas aeruginosa (ATCC 9027), Salmonella Typhimurium (ATCC 14028), Staphylococcus aureus (ATCC 6538) e Staphylococcus epidermidis (ATCC 12228). Os espectros de FTIR-ATR forneceram informações quanto à composição de proteínas, DNA/RNA, lipídeos e carboidratos provenientes do crescimento microbiano. As identificações microbianas fornecidas pelo modelo PCA/LDA baseado no método FTIR-ATR foram compatíveis com aquelas obtidas pelos métodos microbiológicos convencionais. O método de identificação microbiana rápida por FTIR-ATR foi validado quanto à sensibilidade (93,5%), especificidade (83,3%) e limite de detecção (17-23 UFC/mL de amostra). Portanto, o MMR proposto neste trabalho pode ser usado para fornecer uma identificação rápida de contaminantes microbianos em produtos farmacêuticos. / Microbiological quality of pharmaceuticals is fundamental in ensuring efficacy and safety of medicines. Conventional methods for microbial identification in non-sterile drugs are widely used, however are time-consuming and laborious. The aim of this paper was to develop a rapid microbiological method (RMM) for identification of contaminants in pharmaceutical products using Fourier transform infrared with attenuated total reflectance spectrometry (FTIR-ATR). Principal components analysis (PCA) and linear discriminant analysis (LDA) were used to obtain a predictive model with capable to distinguish Bacillus subtilis (ATCC 6633), Candida albicans (ATCC 10231), Enterococcus faecium (ATCC 8459), Escherichia coli (ATCC 8739), Micrococcus luteus (ATCC 10240), Pseudomonas aeruginosa (ATCC 9027), Salmonella Typhimurium (ATCC 14028), Staphylococcus aureus (ATCC 6538), and Staphylococcus epidermidis (ATCC 12228) microbial growth. FTIR-ATR spectra provide information of protein, DNA/RNA, lipids, and carbohydrates constitution of microbial growth. Microbial identification provided by PCA/LDA based on FTIR-ATR method were compatible to those obtained using conventional microbiological methods. FTIR-ATR method for rapid identification of microbial contaminants in pharmaceutical products was validated by assessing the sensitivity (93.5%), specificity (83.3%), and limit of detection (17-23 CFU/mL of sample). Therefore, the RMM proposed in this work may be used to provide a rapid identification of microbial contaminants in pharmaceutical products.

On suppose que des vecteurs de données de grande dimension arrivant en ligne sont des observations indépendantes d'un vecteur aléatoire. Dans le second chapitre, ce dernier, noté Z, est partitionné en deux vecteurs R et S et les observations sont supposées identiquement distribuées. On définit alors une méthode récursive d'estimation séquentielle des r premiers facteurs de l'ACP projetée de R par rapport à S. On étudie ensuite le cas particulier de l'analyse canonique, puis de l'analyse factorielle discriminante et enfin de l'analyse factorielle des correspondances. Dans chacun de ces cas, on définit plusieurs processus spécifiques à l'analyse envisagée. Dans le troisième chapitre, on suppose que l'espérance En du vecteur aléatoire Zn dont sont issues les observations varie dans le temps. On note Rn = Zn - En et on suppose que les vecteurs Rn forment un échantillon indépendant et identiquement distribué d'un vecteur aléatoire R. On définit plusieurs processus d'approximation stochastique pour estimer des vecteurs directeurs des axes principaux d'une analyse en composantes principales (ACP) partielle de R. On applique ensuite ce résultat au cas particulier de l'analyse canonique généralisée (ACG) partielle après avoir défini un processus d'approximation stochastique de type Robbins-Monro de l'inverse d'une matrice de covariance. Dans le quatrième chapitre, on considère le cas où à la fois l'espérance et la matrice de covariance de Zn varient dans le temps. On donne finalement des résultats de simulation dans le chapitre 5 / High dimensional data are supposed to be independent on-line observations of a random vector. In the second chapter, the latter is denoted by Z and sliced into two random vectors R et S and data are supposed to be identically distributed. A recursive method of sequential estimation of the factors of the projected PCA of R with respect to S is defined. Next, some particular cases are investigated : canonical correlation analysis, canonical discriminant analysis and canonical correspondence analysis ; in each case, several specific methods for the estimation of the factors are proposed. In the third chapter, data are observations of the random vector Zn whose expectation En varies with time. Let Rn = Zn - En be and suppose that the vectors Rn form an independent and identically distributed sample of a random vector R. Stochastic approximation processes are used to estimate on-line direction vectors of the principal axes of a partial principal components analysis (PCA) of ~Z. This is applied next to the particular case of a partial generalized canonical correlation analysis (gCCA) after defining a stochastic approximation process of the Robbins-Monro type to estimate recursively the inverse of a covariance matrix. In the fourth chapter, the case when both expectation and covariance matrix of Zn vary with time n is considered. Finally, simulation results are given in chapter 5

Neste trabalho foi utilizado um método matemático para classificar registros de potencial e corrente de ensaios de corrosão na técnica de amperimetria de resistência nula (ZRA). Foi aplicado o método estatístico de múltiplas variáveis simples chamado Análise dos Componentes Principais (PCA), cujo objetivo principal foi identificar padrões nestes dados de ruído eletroquímico. Foram testados o aço carbono UNS G10200, os aços inoxidáveis austenítico UNS S31600 e o superduplex UNS S32750 em meios de ácido sulfúrico (5% H2SO4), cloreto férrico (0,1 mol/L FeCl3) e hidróxido de sódio (0,1% NaOH). Os ensaios foram replicados com oito repetições para se ter reprodutibilidade e conhecimento dos aspectos estatísticos envolvidos. Os resultados mostraram que a análise de componentes principais pode ser utilizada como uma ferramenta para analisar sinais de ruído eletroquímico, identificando os clusters dos comportamentos potencial-tempo, corrente-tempo e acessoriamente identificar os outliersdos registros temporais. / In this study, a mathematical method was used to classify potential and current records of electrochemical noise tests in zero resistance ammeter (ZRA) configuration. The statistical method of multiple simple variables called Principal Components Analysis (PCA) was applied to identify patterns in these electrochemical noise data. The carbon steel UNS G10200, the austenitic stainless steels UNS S31600 and the super duplex UNS S32750 were tested in the solutions of sulfuric acid (5% H2SO4), ferric chloride (0.1 mol/L FeCl3) and sodium hydroxide (0.1% NaOH). The tests were replicated with eight repetitions to obtain reproducibility of the relatedstatistical aspects. The results showed that the principal components analysis could be used as a tool to analyze electrochemical noise signals, identifying behavior clusters of potential-time, current-time and also identifying the outliers in time domain.

Made available in DSpace on 2014-12-17T15:42:03Z (GMT). No. of bitstreams: 1 MariaFPV.pdf: 6083202 bytes, checksum: 8b9199df5753800b615ab0a90bae3e8e (MD5) Previous issue date: 2007-12-10 / Heavy metals can cause problems of human poisoning by ingestion of contaminated food, and the environment, a negative impact on the aquatic fauna and flora. And for the presence of these metals have been used for aquatic animals biomonitoramento environment. This research was done in order to assess the environmental impact of industrial and domestic sewage dumped in estuaries potiguares, from measures of heavy metals in mullet. The methods used for these determinations are those in the literature for analysis of food and water. Collections were 20 samples of mullet in several municipality of the state of Rio Grande do Norte, from the estuaries potiguares. Were analyzed the content of humidity, ash and heavy metals. The data were subjected to two methods of exploratory analysis: analysis of the main components (PCA), which provided a multivariate interpretation, showing that the samples are grouped according to similarities in the levels of metals and analysis of hierarchical groupings (HCA), producing similar results. These tests have proved useful for the treatment of the data producing information that would hardly viewed directly in the matrix of data. The analysis of the results shows the high levels of metallic species in samples Mugil brasiliensis collected in Estuaries /Potengi, Piranhas/A?u, Guara?ra / Papeba / Ar?s and Curimata? / Os metais pesados podem provocar problemas de intoxica??o humana pela ingest?o de alimentos contaminados e para o meio ambiente, uma repercuss?o negativa ? fauna e flora aqu?ticas. E para detectar a presen?a destes metais t?m-se utilizado animais aqu?ticos para o biomonitoramento ambiental. Esta pesquisa foi feita com o intuito de se avaliar o impacto ambiental de esgotos dom?sticos e industriais despejados nos estu?rios potiguares, a partir das medidas de metais pesados em tainha. Os m?todos utilizados para estas determina??es s?o aqueles constantes da literatura para an?lise de alimentos e de ?gua. Foram coletas 20 amostras de tainha em diversos munic?pios do Estado do Rio Grande do Norte, oriundas dos estu?rios potiguares. Foram analisados os teores de umidade, cinzas e metais pesados. Os dados foram submetidos a dois m?todos de an?lises explorat?rios: an?lise de componentes principais (PCA), que proporcionou uma interpreta??o multivariada, mostrando que as amostras s?o agrupadas de acordo com as similaridades de teores de metais e an?lise hier?rquica de agrupamentos (HCA), produzindo resultados semelhantes. Estas an?lises mostraram-se ?teis para o tratamento dos dados produzindo informa??es que dificilmente seriam visualizados diretamente na matriz de dados. A an?lise dos resultados mostra os altos teores de esp?cies met?licas em amostras coletadas em tainhas nos Estu?rios Potengi, Piranhas/A?u, Guara?ra/Papeba/Ares e Curimata?

Magistro baigiamajame darbe išanalizuota ir įvertinta valstybių kredito reitingų suteikimo metodologija, šio proceso kritika, pateikti pasiūlymai esamoms problemoms spręsti. Atlikta koreliacinė, regresinė, pagrindinių komponenčių analizė ir pasinaudojus trijų Baltijos šalių – Lietuvos, Latvijos ir Estijos, pavyzdžiu surasti trys atskiri modeliai, tiksliausiai prognozuojantys minėtų valstybių kredito reitingus, remiantis makroekonominiais rodikliais. Pirmoje darbo dalyje teoriniu aspektu nagrinėjama kredito reitingo samprata, jo reikšmė finansų rinkoms, apibrėžiamos priežastys, lemiančios kredito reitingų trūkumus ir pateikiami tobulinimo siūlymai. Antroje dalyje analizuojamos trijų pagrindinių kredito reitingo agentūrų – Standard and Poor‘s, Fitch ir Moody‘s valstybių kredito reitingo suteikimo metodologijos, tiriama mokslinė literatūra, nagrinėjanti kredito reitingo priklausomybę nuo makroekonominių rodiklių, pateikiamas tyrimo modelis, nagrinėjamos su juo susijusios problemos, apibrėžiama darbo eiga. Trečioje dalyje sudaromos tiesinės daugianarės regresijos lygtys, naudojamos prognozuoti Lietuvos, Latvijos ir Estijos kredito reitingą, atliekamas ateities kredito reitingų prognozavimas remiantis faktiniais 2012 m. IV ketvirčio duomenimis ir numatomais scenarijais. / Master's Work analyzed and evaluated methodology of sovereign credit ratings, the critique of the process itself and proposed solutions for existing problems. Correlation, regression and principal components analysis were used to determine distinct models for the three Baltic states – Lithuania, Latvia and Lithuania, that accurately predicts future credit ratings based on macro-economic indicators. The first part examines theoretical aspect of the concept of credit rating, its value to the global financial markets, defines the causes of the credit rating errors, presents possible solutions for the failures of credit ratings. In the second section methodologies used by Standard and Poor's, Fitch and Moody's to determine sovereign credit ratings are analyzed, scientific literature on the dependence of credit rating and macro-economic indicators are examined, research model and problems associated with it are presented, workflow is defined. In the third part linear multiple regression equations are derived which are used to predict future credit ratings of Lithuania, Latvia and Estonia, future credit ratings predictions are carried out based on actual year 2012 fourth quarter data and future scenarios.