Ph. D.

This dissertation is a set of related papers on the application of the "principle of statistical adequacy" to single and multi-equation econometric models. The first chapter lays out the intended scope of the dissertation and defines the principle of statistical adequacy. The second chapter reviews the formulation of tests of statistical adequacy for multivariate models, and describes the implementation of these tests. The first approach that is discussed is to select particular functions of the variables involved that should be orthogonal under the null hypothesis of no misspecification, and the sample analog of these functions is used as a basis for constructing misspecification tests. As an extension of this idea, it is argued that viewing the model in explicit probabilistic terms provides a basis for developing a set of orthogonality conditions that can be tested in terms of all the probabilistic assumptions underlying the model. The formulation of misspecification tests via auxiliary regressions using general polynomial functions and the implementation of these tests via a menu-driven econometric modeling computer program is described. The third chapter reports the results of an empirical application of the principle of Statistical adequacy to the modeling of inflation/unemployment trade-offs for the U.S. Using a Statistically adequate “reduced-form" as the basis, a number of competing theoretical models are considered. The use of graphical techniques and formal misspecification tests in determining the adequacy of the statistical model are emphasized. It is found that none of the competing theoretical explanations of aggregate labor market behavior are acceptable in terms of the over-identifying restrictions imposed or their own statistical adequacy. The final chapter is an example of how one might proceed when a specification failures the criteria of statistical adequacy. For U.S. interest rates, it is shown that linear-homoskedastic autoregessions do not adequately account for the leptokurtosis and non-linear temporal dependence in the data. Using the evidence provided by preliminary data analysis as a guide, the Student’s t autoregressive model with dynamic heteroskedasticity is estimated for the log differences in three interest rate series. The estimation and misspecification testing results suggest that the STAR model adequately accounts for the probabilistic features of the data: bell-shape symmetry; leptokurtosis; first and second-order temporal dependence. In contrast, a number of other heteroskedastic specifications are estimated, and found to be statistically inadequate. / Ph. D.

Traditionally, single species toxicity tests have been the primary tool for assessment of hazard of toxic substances in aquatic ecosystems. These tests are inadequate for accurately reflecting the impact of toxicants on the community structure inherent in ecosystems. Multispecies microcosm experiments are gaining widespread acceptance as an important vehicle in understanding the nature and magnitude of effects for more complex systems. Microcosm experiments are complex and costly to conduct. Consequently, sample sizes are typically small (8-20 replicates). In addition, these experiments are difficult to analyze due to their multivariate and repeated measures nature. Working under the constraint of small sample sizes, we develop inferential as well as diagnostic methods that detect and measure community changes as a result of an intervention (i.e. toxicant), and assess the importance of individual species. A multi-factorial simulation analysis is used to compare several methods. The Multi-Response Permutation Procedure (MRPP) and a regression method incorporating a correlation structure are found to be the most powerful procedures for detecting treatment differences. The MRPP is particularly suited to experiments with replication and when the response variable may not be normally distributed. The regression model for dissimilarity data has the advantage of enabling direct estimation of many parameters not possible with the MRPP as well as the magnitude of treatment effects. A stepwise dependent variable selection algorithm with a selection criterion based on a conditional p-value argument is proposed and applied to a real data set. It is seen to have advantages over other methods for assessing species importance. / Ph. D.

Two prominent monitoring procedures in statistical quality control are the p-chart for the proportion of items defective, and the c-chart, for the number of defects per item. These procedures are reconsidered, and some extensions are examined for monitoring processes with multiple attributes. Some relevant distribution theory is reviewed, and some new results are given. The distributions considered are multivariate versions of the binomial, Poisson, and chi-squared distributions, plus univariate and multivariate generalized Poisson distributions. All of these distributions prove useful in the discussion of attribute control charts. When quality standards are known, p-charts and c-charts are shown to have certain optimal properties. Generalized p-charts, for monitoring multinomial processes, and generalized c-charts are introduced. Their properties are shown to depend upon multivariate chi-squared and generalized Poisson distributions, respectively. Various techniques are considered for monitoring multivariate Bernoulli, Poisson, multinomial, and generalized Poisson processes. Omnibus procedures are given, and some of their asymptotic properties are derived. Also examined are diagnostic procedures based upon both small- and large-sample. / Ph. D.

Sappi is one of the leading producer and supplier of Eucalyptus pulp to the world market. It is also a great contributor to South Africa economy in terms of employment opportunity to the rural people through its large plantation and export earnings. Pulp mills production of quality wood pulp is mainly affected by the supply of non uniform raw material namely Eucalyptus tree supply from various plantations. Improvement in quality of the pulp depends directly on the improvement on the quality of the raw materials. Knowing factors which affect the pulp quality is important for tree breeders. Thus, the main objective of this research is first to determine which of the anatomical, chemical and pulp properties of wood are significant factors that affect pulp properties namely viscosity, brightness and yield. Secondly the study will also investigate the effect of the difference in plantation location and site quality, trees age and species type difference on viscosity, brightness and yield of wood pulp. In order to meet the above mentioned objectives, data for this research was obtained from Sappi’s P186 trial and other two published reports from the Council for Scientific and Industrial Research (CSIR). Principal component analysis, cluster analysis, multiple regression analysis and multivariate linear regression analysis were used. These statistical analysis methods were used to carry out mean comparison of pulp quality measurements based on viscosity, brightness and yield of trees of different age, location, site quality and hybrid type and the results indicate that these four factors (age, location, site quality and hybrid type) and some anatomical and chemical measurements (fibre lumen diameter, kappa number, total hemicelluloses and total lignin) have significant effect on pulp quality measurements. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

Palynology involves the study of past climatic and environmental changes through changes in the relative frequencies of different pollen types through time. Several multivariate statistical methods are suggested which can help in the description of patterns within pollen data. These techniques are based on comparisons between samples. Samples were compared using the product-moment correlation coefficient computed from data which had been subjected to a centering transformation. The methods are described using a geometric model. If there are m samples and n pollen types, then the data can be regarded as a set of m points in an n-dimensional space. Cluster analysis produces a dendrograph or clustering tree in which samples are grouped with other samples on the basis of their similarity to each other. Principal component analysis produces a set of variates which are linear combinations of the pollen samples, are uncorrelated with each other, and do the best job of describing the data using a minimum number of dimensions. This method is useful in reducing the dimensionality of data sets. Varimax rotation acts on a subset of the principal components to make them easier to interpret. Discriminant analysis is used to find the best way to tell groups of samples apart, where the groups are known a priori. Once a means of discrimination among groups has been established using samples whose groups are known, unknown samples may be classified into the original groups. Canonical analysis produces a way to display the maximum separation between groups in a graphic manner. Examples of applications of these methods in palynology are shown using data from Osgood Swamp, California, and from southern Arizona. These methods offer the advantages of reproducibility of results and speed in pattern description. Once the patterns in the data have been described, however, their interpretation must be done by the palynologist.

This work concerns the fractionation of phosphorus present in sediments from the Macela Reservoir, located in the city of Itabaiana (Sergipe State, Brazil). Two sediment cores were obtained, each to a depth of approximately 30 cm, which were divided into 5 cm sections. The analytical method employed a Standards, Measurements, and Testing (SMT) protocol, in which the phosphorus was split into the fractions: total (PT), inorganic (PI), organic (PO), non-apatite (PNAP), and apatite (PAP). The technique was validated in terms of the limits of detection (DL) and quantification (QL) for each fraction. No significant contamination was observed. The accuracy was in the range 99-101%, and the relative standard deviation (RSD) was better than 2%. The measured phosphorus concentrations were in the ranges 441.60-1335.47 µg g-1 (PT), 409.54-1209.86 µg g-1 (PI), and 21.35-195.87 µg g-1 (PO). For the inorganic forms, the concentrations of PNAP and PAP were in the ranges 106.82-541.09 µg g-1 and 238.56-698.01 µg g-1, respectively. The concentrations of the phosphorus fractions were highest in Core 2. The contents of Fe, Al, Ca, and Corg were 3.45-4.95%, 4.85-7.73%, 1.02-1.89%, and 1.88-8.55%, respectively. Correlation analysis using the Spearman test identified iron and aluminum as the most important controlling factors for P in the sediments studied. The application of principal components analysis (PCA) and hierarchical clustering analysis (HCA) to the measured parameters divided the sediment samples into two groups, according to their similarities. This was also confirmed using analysis of variance (ANOVA, p<0.05). / Neste trabalho foi realizado o fracionamento do fósforo em sedimentos do Reservatório Macela, localizado na cidade de Itabaiana, Sergipe, Brasil. Foram tomados dois testemunhos com profundidade de aproximadamente 30 cm cada, que foram seccionados de 5 cm em 5 cm. O método analítico utilizado foi o Protocolo desenvolvido pelo Standards, Measurements and Testing (SMT), que fracionou o fósforo nos sedimentos em total (PT), inorgânico (PI), orgânico (PO), não apatita (PNAP) e apatita (PAP). A validação da metodologia foi verificada através dos valores de limite de detecção (LD) e de limite de quantificação (LQ) para PT, PI, PO, PNAP e PAP, onde se observou que não houve contaminação significativa. A exatidão do método foi conferida através dos valores de concordância variando 99 a 101% e o desvio padrão relativo (RSD) foi melhor que 2%. A concentração de P variaram entre 441,60 e 1335,47 µg g-1 para PT, entre 409,54 e 1209,86 µg g-1 para PI e entre 21,35 e 195,87 µg g-1 para Po. Para as formas inorgânicas o valor das concentrações de PNAP variou de 106,82 e 541,09 µg g-1 e de PAP variou de 238,56 a 698,01 µg g-1. As concentrações das frações de fósforo nos sedimentos analisados foram maiores no testemunho II. Os conteúdos de Fe, Al, Ca e Corg variaram de 3,45 a 4,95 %, de 4,85 a 7,73 %, de 1,02 a 1,89 % e de 1,88 a 8,55 %. A matriz de correlação de Sperman identificou o ferro e o alumínio como os fatores controladores mais importantes dos P nos sedimentos analisados. A análise de componentes principais (PCA) e analise de agrupamento hierárquico (HCA), aplicada aos parâmetros medidos, dividiu as amostras de sedimentos em dois grupos, de acordo com suas similaridades. Esta tendência foi confirmada pela análise de variância (ANOVA, p< 0,05).

Survival analysis pertains to a statistical approach designed to take into account the amount of time an experimental unit contributes to a study. A Mayo Clinic study of 418 Primary Biliary Cirrhosis patients during a ten year period was used. The Kaplan-Meier Estimator, a non-parametric statistic, and the Cox Proportional Hazard methods were the tools applied. Kaplan-Meier results include total values/censored values.

<p>Recent advances in technology have allowed researchers to collect high-dimensional biological data simultaneously. In genomic studies, for instance, measurements from tens of thousands of genes are taken from individuals across several experimental groups. In time course microarray experiments, gene expression is measured at several time points for each individual across the whole genome resulting in massive amount of data. In such experiments, researchers are faced with two types of high-dimensionality. The first is global high-dimensionality, which is common to all genomic experiments. The global high-dimensionality arises because inference is being done on tens of thousands of genes resulting in multiplicity. This challenge is often dealt with statistical methods for multiple comparison, such as the Bonferroni correction or false discovery rate (FDR). We refer to the second type of high-dimensionality as gene specific high-dimensionality, which arises in time course microarry experiments due to the fact that, in such experiments, sample size is often smaller than the number of time points ($n</p> <p>In this thesis, we use the growth curve model (GCM), which is a generalized multivariate analysis of variance (GMANOVA) model, and propose a moderated test statistic for testing a special case of the general linear hypothesis, which is specially useful for identifying genes that are expressed. We use the trace test for the GCM and modify it so that it can be used in high-dimensional situations. We consider two types of moderation: the Moore-Penrose generalized inverse and Stein's shrinkage estimator of $ S $. We performed extensive simulations to show performance of the moderated test, and compared the results with original trace test. We calculated empirical level and power of the test under many scenarios. Although the focus is on hypothesis testing, we also provided moderated maximum likelihood estimator for the parameter matrix and assessed its performance by investigating bias and mean squared error of the estimator and compared the results with those of the maximum likelihood estimators. Since the parameters are matrices, we consider distance measures in both power and level comparisons as well as when investigating bias and mean squared error. We also illustrated our approach using time course microarray data taken from a study on Lung Cancer. We were able to filter out 1053 genes as non-noise genes from a pool of 22,277 genes which is approximately 5\% of the total number of genes. This is in sync with results from most biological experiments where around 5\% genes are found to be differentially expressed.</p> / Master of Science (MSc)

Nitrogen-fixing bacteria in soybean nodules convert atmospheric nitrogen to plant-available forms in exchange for carbon from the plant, but other non-nitrogen-fixing bacteria also reside in nodules, and their role in the nodule is not well understood. This study was conducted to determine the effect of three non-nitrogen-fixing Pseudomonas spp. strains isolated from nodules on soybean, and we hypothesized these strains benefit soybean. A greenhouse study in which two cultivars of soybean (Asgrow AG46X6 and Pioneer P48A60X) were treated with three fluorescent Pseudomonas spp. strains (referred to in this study as Bullseye, Pancake, and Starfish) and an uninoculated control. Soybeans were harvested at two time points: the R2/R3 growth stage and the R6 growth stage. Following each harvest, measures of growth, yield, and nitrogen fixation were taken, and data were analyzed using two non-parametric, multivariate analyses: multiple response permutation procedure (MRPP) and permutational multivariate analysis of variance (PERMANOVA). Both analyses showed soybeans of both cultivars treated with Pancake differed from controls following the first harvest but not the second. When analyzed individually, most metrics for growth, yield, and nitrogen fixation following the first harvest were not significantly different between Pancake and control treatments, but Pancake treatment means were still generally higher than controls. If metrics are considered collectively in conjunction with the results of the multivariate analyses, the results show Pancake generally increased soybean growth and nitrogen fixation. These findings support the hypothesis that non-nitrogen-fixing bacteria from nodules benefit plants, and such bacteria have the potential to serve as biofertilizers. / Master of Science in Life Sciences / Soybeans are one of the most commonly grown crops in the world, and nitrogen-fixing bacteria colonize the roots of soybeans and initiate the formation of spherical nodules attached to the roots. Inside the nodules, these bacteria convert atmospheric nitrogen to plant-available forms in exchange for sugar from the plant, and such bacteria reduce the need to add nitrogen fertilizer to agricultural fields. Other non-nitrogen-fixing bacteria also reside in nodules, but their role in the nodule is not well understood. If these bacteria benefit soybeans, they have the potential to serve as biofertilizers (microbial inoculants that promote plant growth). This study was conducted to determine whether non-nitrogen-fixing bacteria isolated from nodules benefit soybean. A greenhouse study in which two cultivars of soybean (Asgrow AG46X6 and Pioneer P48A60X) were grown in soil and were either left uninoculated or were inoculated with one of three strains of bacteria from the genus, Pseudomonas (referred to in this study as Bullseye, Pancake, and Starfish). Following harvest, measures of growth, yield, and nitrogen fixation were taken, and data showed the bacteria generally benefited the soybean plants. Although, these results showed the bacteria benefitted the plants, field trials and further testing in the greenhouse should be conducted before using these bacteria as commercial biofertilizers. Additionally, the effects of other non-nitrogen-fixing nodule bacteria on soybeans should also be tested to identify other beneficial strains, and the cost of production should be compared to the potential gains of using such bacteria before they are developed into biofertilizers.