In developing an understanding of real-world problems, researchers develop mathematical and statistical models. Various model selection methods exist which can be used to obtain a mathematical model that best describes the real-world situation in some or other sense. These methods aim to assess the merits of competing models by concentrating on a particular criterion. Each selection method is associated with its own criterion and is named accordingly. The better known ones include Akaike's Information Criterion, Mallows' Cp and cross-validation, to name a few. The value of the criterion is calculated for each model and the model corresponding to the minimum value of the criterion is then selected as the "best" model. / Mathematical Sciences / M. Sc. (Statistics)

The detection of multiple outliers can be interpreted as a model selection problem. Models that can be selected are the null model, which indicates an outlier free set of observations, or a class of alternative models, which contain a set of additional bias parameters. A common way to select the right model is by using a statistical hypothesis test. In geodesy data snooping is most popular. Another approach arises from information theory. Here, the Akaike information criterion (AIC) is used to select an appropriate model for a given set of observations. The AIC is based on the Kullback-Leibler divergence, which describes the discrepancy between the model candidates. Both approaches are discussed and applied to test problems: the fitting of a straight line and a geodetic network. Some relationships between data snooping and information criteria are discussed. When compared, it turns out that the information criteria approach is more simple and elegant. Along with AIC there are many alternative information criteria for selecting different outliers, and it is not clear which one is optimal.

Στην παρούσα εργασία μελετούμε τη σχέση μεταξύ χρηματιστηριακών αποδόσεων και δείκτη εμπιστοσύνης στις 27 χώρες-μέλη της ΕΕ για τα έτη 1985-2006. Βρήκαμε ότι για το μεγαλύτερο μέρος των χωρών της ΕΕ εμφανίζεται θετική συσχέτιση μεταξύ αποδόσεων και δείκτη εμπιστοσύνης του καταναλωτή στον βραχυχρόνιο ορίζοντα. Οι μεταβολές και στους δύο δείκτες τείνουν να κινούνται παράλληλα στην ίδια περίοδο, με εξαίρεση την πλειοψηφία των νεοεισελθέντων χωρών. Στον μακροπρόθεσμο ορίζοντα, βρήκαμε ότι για τις περισσότερες χώρες ο συντελεστής γίνεται σχεδόν μηδενικός. Για το μεγαλύτερο μέρος των χωρών της ΕΕ υφίσταται σχέση αιτιότητας μεταξύ των μεταβλητών, με τις αποδόσεις να προκαλούν κατά Granger τον δείκτη εμπιστοσύνης του καταναλωτή και τον δείκτη οικονομικής εμπιστοσύνης, αλλά το αντίστροφο δεν ισχύει. Αμφίδρομη σχέση αιτιότητας μεταξύ αποδόσεων και εμπιστοσύνης των καταναλωτών παρατηρείται μόνο για την Γαλλία οριακά, ενώ για την ΕΕ βρήκαμε οτι υπάρχει αμφίδρομη σχέση αιτιότητας μεταξύ αποδόσεων και δείκτη οικονομικής εμπιστoσύνης. / This paper studies the relationship between stock market developments and confidence index for the 27 EU countries - members over the years 1985-2006. We found that for the majority of the EU countries exists positive correlation between the stock market index and the confidence indicators (consumer confidence indicator and economic sentiment indicator) in the short horizon. The changes between these indexes tempt to move in the same direction contemporaneously and in the short horizon (of 1 month), with the new EU members to be an exception. The correlation becomes almost zero in the long horizon. For the most of the EU countries there is causality between the variables. Stock returns in general Granger-cause the Consumer Confidence Index and the Economic Sentiment Indicator, but not vice versa. We found also that there is feedback causality relationship between stock returns and confidence for France and the EU as a whole.

In developing an understanding of real-world problems, researchers develop mathematical and statistical models. Various model selection methods exist which can be used to obtain a mathematical model that best describes the real-world situation in some or other sense. These methods aim to assess the merits of competing models by concentrating on a particular criterion. Each selection method is associated with its own criterion and is named accordingly. The better known ones include Akaike's Information Criterion, Mallows' Cp and cross-validation, to name a few. The value of the criterion is calculated for each model and the model corresponding to the minimum value of the criterion is then selected as the "best" model. / Mathematical Sciences / M. Sc. (Statistics)

The detection of multiple outliers can be interpreted as a model selection problem. Models that can be selected are the null model, which indicates an outlier free set of observations, or a class of alternative models, which contain a set of additional bias parameters. A common way to select the right model is by using a statistical hypothesis test. In geodesy data snooping is most popular. Another approach arises from information theory. Here, the Akaike information criterion (AIC) is used to select an appropriate model for a given set of observations. The AIC is based on the Kullback-Leibler divergence, which describes the discrepancy between the model candidates. Both approaches are discussed and applied to test problems: the fitting of a straight line and a geodetic network. Some relationships between data snooping and information criteria are discussed. When compared, it turns out that the information criteria approach is more simple and elegant. Along with AIC there are many alternative information criteria for selecting different outliers, and it is not clear which one is optimal.

Made available in DSpace on 2015-04-22T22:16:08Z (GMT). No. of bitstreams: 1 Dissertacao Jose Mir Final.pdf: 1095442 bytes, checksum: bd21928f8f84d5235ab2e76eb5c5f0cb (MD5) Previous issue date: 2009-04-17 / FAPEAM - Fundação de Amparo à Pesquisa do Estado do Amazonas / The present work aims to evaluate some information criteria for the selection of models in the context of finite mixtures of skew-normal distributions. The analyzed criteria are the Akaike s Information Criterion - AIC, the Bayesian Information Criterion - BIC and the Efficient Detection Criterion - EDC. The evaluation concerning the performance presented by these criteria was obtained through a simulation study, on which the EM algorithm is required to find the maximum likelihood estimates of for the parameters of the model where the criteria are applied. It was also performed an experiment for the application of the theory developed, modeling a real data set previously analyzed in the specific literature. The results obtained point that, in an asymptotic sense, the three criteria tend to correctly evaluate the number of necessary components, but for small samples the AIC presents inferior performance than BIC or EDC. / Este trabalho tem por objetivo avaliar alguns critérios de informação para seleção de modelos no contexto de misturas finitas de normais assimétricas. Os critérios analisados foram o Critério de Informação de Akaike-AIC , Critério de Informação Bayesiano - BIC e Critério de Determinação Eficiente - EDC . A avaliação feita a respeito do desempenho apresentado por estes critérios se deu através de um estudo de simulação, em que utilizamos o algoritmo EM para encontrarmos as estimativas de máxima verossimilhança para os parâmetros do modelo com as quais empregamos os critérios. Foi também realizado uma aplicação da teoria desenvolvida para uma modelagem com dados reais utilizando dois conjuntos de dados já analisado anteriormente na literatura. Os resultados obtidos indicaram que, assintoticamente, os três critérios tendem a avaliar corretamente o número de componentes necessárias, mas para amostras pequenas o AIC apresenta desempenho inferior ao BIC e EDC, sendo que os dois últimos apresentam desempenho muito semelhante.

Crystallographic image processing (CIP) is a technique first used to aid in the structure determination of periodic organic complexes imaged with a high-resolution transmission electron microscope (TEM). The technique has subsequently been utilized for TEM images of inorganic crystals, scanning TEM images, and even scanning probe microscope (SPM) images of two-dimensional periodic arrays. We have written software specialized for use on such SPM images. A key step in the CIP process requires that an experimental image be classified as one of only 17 possible mathematical plane symmetry groups. The current methods used for making this symmetry determination are not entirely objective, and there is no generally accepted method for measuring or quantifying deviations from ideal symmetry. Here, we discuss the crystallographic symmetries present in real images and the general techniques of CIP, with emphasis on the current methods for symmetry determination in an experimental 2D periodic image. The geometric Akaike information criterion (AIC) is introduced as a viable statistical criterion for both quantifying deviations from ideal symmetry and determining which 2D Bravais lattice best fits the experimental data from an image being processed with CIP. By objectively determining the statistically favored 2D Bravais lattice, the determination of plane symmetry in the CIP procedure can be greatly improved. As examples, we examine scanning tunneling microscope images of 2D molecular arrays of the following compounds: cobalt phthalocyanine on Au (111) substrate; nominal cobalt phthalocyanine on Ag (111); tetraphenoxyphthalocyanine on highly oriented pyrolitic graphite; hexaazatriphenylene-hexacarbonitrile on Ag (111). We show that the geometric AIC procedure can unambiguously determine which 2D Bravais lattice fits the experimental data for a variety of different lattice types. In some cases, the geometric AIC procedure can be used to determine which plane symmetry group best fits the experimental data, when traditional CIP methods fail to do so.

This thesis aims to identify main driving market risk factors of different strategies implemented by hedge funds by looking at correlation coefficients, implementing Principal Component Analysis and analyzing "loadings" for first three principal components, which explain the largest portion of the variation of hedge funds' returns. In the next step, a stepwise regression through iteration process includes and excludes market risk factors for each strategy, searching for the combination of risk factors which will offer a model with the best "fit", based on The Akaike Information Criterion - AIC and Bayesian Information Criterion - BIC. Lastly, to avoid counterfeit results and overcome model uncertainty issues a Bayesian Model Average - BMA approach was taken. Key words: Hedge Funds, hedge funds' strategies, market risk, principal component analysis, stepwise regression, Akaike Information Criterion, Bayesian Information Criterion, Bayesian Model Averaging Author's e-mail: aleksaradosavcevic@gmail.com Supervisor's e-mail: mp.princ@seznam.cz

In this paper, we examine the feasibility of extending the Akaike information criterion (AIC) for deterministic systems as a potential model selection criteria for stochastic models. We discuss the implementation method for three different classes of stochastic models: continuous time Markov chains (CTMC), stochastic differential equations (SDE), and random differential equations (RDE). The effectiveness and limitations of implementing the AIC for comparison of stochastic models is demonstrated using simulated data from the three types of models and then applied to experimental longitudinal growth data for algae.

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