É comum o estudo da estabilidade fenótipica em genoótipos de cana-de-açúcar. Varias são as metodologias para estudar a interação genótipos x ambientes (G x E). O desafio para os melhoristas é encontrar variedades de cana-de-açúcar com desempenho superior em diversos ambientes, ou seja, que sejam altamente produtivas e também responsivas com a melhoria do ambiente. O estudo das metodologias permite verificar se determinada técnica biométrica é eficiente para expressar o comportamento de genótipos em vários ambientes e tambem permite aprimorá-las para que as conclusões sejam mais confiáveis. Este trabalho teve como objetivo comparar dois métodos de regressão utilizados para avaliar a estabilidade fenótipica em variedades de cana-de-açúcar: o linear, de Cruz, Torres e Vencovsky (1989) e o não-linear, de Toler e Burrows (1998). Foram utilizados dados da variável tonelada de cana por hectare - TCH, fornecidos pelo Programa de Melhoramento Genetico da Cana-de- Acucar da UFSCar, compreendendo sete locais e 18 genótipos de cana-de-açúcar. Quando se realizou o enquadramento dos genotipos nos diferentes grupos, 17 genotipos dos 18 avaliados enquadraram-se nos mesmos grupos em ambos os métodos. Os coeficientes de determinação foram similares, sendo que 11 genótipos apresentaram melhor ajuste ao modelo de Cruz et al., enquanto que este numero foi de sete para o modelo de Toler e Burrows. As análises indicaram que ambas metodologias produziram resultados similares. / It is common to study the phenotypic stability of sugarcane genotypes. There are several methods to study the genotype by environment interaction . The challenge for breeders is to nd varieties of sugarcane with superior performance dierent environments, i.e, that are highly productive and responsive to environmental improvement. The study of methodologies allows to verify whether certain technique biometrics is eective to express the behavior of genotypes in several environments and it also allows improving them so that the conclusions are more reliable. This study aimed to compare two regression methods used to evaluate the phenotypic stability of varieties of sugarcane: the linear method by Cruz, Torres e Vencovsky (1989), and non-linear, by Toler and Burrows (1998). We used the variable data tons of cane per hectare - TCH, which were provided by the Genetic Improvement Program of Sugarcane in UFSCar, including seven locations and 18 genotypes. When genotypes were grouped according to stability and yield, 17 of the 18 genotypes evaluated were classied in the same groups, in both methods. The coecients of determination were similar, 11 genotypes showing better adjustment to the model of Cruz et al., while this number was seven for the Toler and Burrows\' model. The analysis indicated that both methodologies produced similiar results.

É comum o estudo da estabilidade fenótipica em genoótipos de cana-de-açúcar. Varias são as metodologias para estudar a interação genótipos x ambientes (G x E). O desafio para os melhoristas é encontrar variedades de cana-de-açúcar com desempenho superior em diversos ambientes, ou seja, que sejam altamente produtivas e também responsivas com a melhoria do ambiente. O estudo das metodologias permite verificar se determinada técnica biométrica é eficiente para expressar o comportamento de genótipos em vários ambientes e tambem permite aprimorá-las para que as conclusões sejam mais confiáveis. Este trabalho teve como objetivo comparar dois métodos de regressão utilizados para avaliar a estabilidade fenótipica em variedades de cana-de-açúcar: o linear, de Cruz, Torres e Vencovsky (1989) e o não-linear, de Toler e Burrows (1998). Foram utilizados dados da variável tonelada de cana por hectare - TCH, fornecidos pelo Programa de Melhoramento Genetico da Cana-de- Acucar da UFSCar, compreendendo sete locais e 18 genótipos de cana-de-açúcar. Quando se realizou o enquadramento dos genotipos nos diferentes grupos, 17 genotipos dos 18 avaliados enquadraram-se nos mesmos grupos em ambos os métodos. Os coeficientes de determinação foram similares, sendo que 11 genótipos apresentaram melhor ajuste ao modelo de Cruz et al., enquanto que este numero foi de sete para o modelo de Toler e Burrows. As análises indicaram que ambas metodologias produziram resultados similares. / It is common to study the phenotypic stability of sugarcane genotypes. There are several methods to study the genotype by environment interaction . The challenge for breeders is to nd varieties of sugarcane with superior performance dierent environments, i.e, that are highly productive and responsive to environmental improvement. The study of methodologies allows to verify whether certain technique biometrics is eective to express the behavior of genotypes in several environments and it also allows improving them so that the conclusions are more reliable. This study aimed to compare two regression methods used to evaluate the phenotypic stability of varieties of sugarcane: the linear method by Cruz, Torres e Vencovsky (1989), and non-linear, by Toler and Burrows (1998). We used the variable data tons of cane per hectare - TCH, which were provided by the Genetic Improvement Program of Sugarcane in UFSCar, including seven locations and 18 genotypes. When genotypes were grouped according to stability and yield, 17 of the 18 genotypes evaluated were classied in the same groups, in both methods. The coecients of determination were similar, 11 genotypes showing better adjustment to the model of Cruz et al., while this number was seven for the Toler and Burrows\' model. The analysis indicated that both methodologies produced similiar results.

Depression, intertwined with sleep deprivation and self-esteem, presents a significant challenge to mental health worldwide. The research shown in this paper employs advanced statistical methodologies to unravel the complex interactions among these factors. Through log-linear homogeneous association, multinomial logistic regression, and generalized linear models, the study scrutinizes large datasets to uncover nuanced patterns and relationships. By elucidating how depression, sleep disturbances, and self-esteem intersect, the research aims to deepen understanding of mental health phenomena. The study clarifies the relationship between these variables and explores reasons for prioritizing depression research. It evaluates how statistical models, such as log-linear, multinomial logistic regression, and generalized linear models, shed light on their intricate dynamics. Findings offer insights into risk and protective factors associated with these variables, guiding tailored interventions for individuals in psychological distress. Additionally, policymakers can utilize these insights to develop comprehensive strategies promoting mental health and well-being at a societal level.

Yellow perch (Perca flavescens) in Lake Erie support valuable commercial and recreational fisheries critical to the local economy and society. The study of yellow perch's temporal and spatial population dynamics is important for both stock assessment and fisheries management. I explore the spatial and temporal variation of the yellow perch population by analyzing the fishery-independent surveys in Lake Erie. Model-based approaches were developed to estimate the relative abundance index, which reflected the temporal variation of the population. I also used design-based approaches to deal with the situation in which population density varied both spatially and temporally. I first used model-based approaches to explore the spatial and temporal variation of the yellow perch population and to develop the relative abundance index needed. Generalized linear models (GLM), spatial generalized linear models (s-GLM), and generalized additive models (GAM) were compared by examining the goodness-of-fit, reduction of spatial autocorrelation, and prediction errors from cross-validation. The relationship between yellow perch density distribution and spatial and environmental factors was also studied. I found that GAM showed the best goodness-of-fit shown as AIC and lowest prediction errors but s-GLM resulted in the best reduction of spatial autocorrelation. Both performed better than GLM for yellow perch relative abundance index estimation. I then applied design-based approaches to study the spatial and temporal population dynamics of yellow perch through both practical data analysis and simulation. The currently used approach in Lake Erie is stratified random sampling (StRS). Traditional sampling designs (simple random sampling (SRS) and StRS) and adaptive sampling designs (adaptive two-phase sampling (ATS), adaptive cluster sampling (ACS), and adaptive two-stage sequential sampling (ATSS)) for fishery-independent surveys were compared. From accuracy and precision aspect, ATS performed better than the SRS, StRS, ACS and ATSS for yellow perch fishery-independent survey data in Lake Erie. Model-based approaches were further studied by including geostatistical models. The performance of the GLM and GAM models and geostatistical models (spatial interpolation) were compared when they are used to analyze the temporal and spatial variation of the yellow perch population through a simulation study. This is the first time that these two types of model- based approaches have been compared in fisheries. I found that arithmetic mean (AM) method was only preferred when neither environment factors nor spatial information of sampling locations were available. If the survey can not cover the distribution area of the population due to biased design or lack of sampling locations, GLMs and GAMs are preferable to spatial interpolation (SI). Otherwise, SI is a good alternative model to estimate relative abundance index. SI has rarely been realized in fisheries. Different models may be recommended for different species/fisheries when we estimate their spatial-temporal dynamics, and also the most appropriate survey designs may be different for different species. However, the criteria and approaches for the comparison of both model-based and design-based approaches will be applied for different species or fisheries. / Ph. D.

Doctor of Philosophy / Department of Statistics / Juan Du / Spatio-temporal and/or multivariate dependence naturally occur in datasets obtained in various disciplines; such as atmospheric sciences, meteorology, engineering and agriculture. There is a great deal of need to effectively model the complex dependence and correlated structure exhibited in these datasets. For this purpose, this dissertation studies methods and application of the spatio-temporal modeling and multivariate computation. First, a collection of spatio-temporal functions is proposed to model spatio-temporal processes which are continuous in space and discrete over time. Theoretically, we derived the necessary and sufficient conditions to ensure the model validity. On the other hand, the possibility of taking the advantage of well-established time series and spatial statistics tools makes it relatively easy to identify and fit the proposed model in practice. The spatio-temporal models with some ARMA discrete temporal margin are fitted to Kansas precipitation and Irish wind datasets for estimation or prediction, and compared with some general existing parametric models in terms of likelihood and mean squared prediction error. Second, to deal with the immense computational burden of statistical inference for multi- ple attributes recorded at a large number of locations, we develop Wendland-type compactly supported covariance matrix function models and propose multivariate covariance tapering technique with those functions for computation reduction. Simulation studies and US tem- perature data are used to illustrate applications of the proposed multivariate tapering and computational gain in spatial cokriging. Finally, to study the impact of weather change on corn yield in Kansas, we develop a spatial functional linear regression model accounting for the fact that weather data were recorded daily or hourly as opposed to the yearly crop yield data and the underlying spatial autocorrelation. The parameter function is estimated under the functional data analysis framework and its characteristics are investigated to show the influential factor and critical period of weather change dictating crop yield during the growing season.

Atkinson 及 Riani 應用前進搜尋演算法來處理百牡利資料中所包含的多重離群值(2001）。在這篇論文中，我們沿用相同的想法來處理在不完整資料下一般線性模型中的多重離群值。這個演算法藉由先填補資料中遺漏的部分，再利用前進搜尋演算法來確認資料中的離群值。我們所提出的方法可以解決處理多重離群值時常會遇到的遮蓋效應。我們應用了一些真實資料來說明這個演算法並得到令人滿意結果。 / Atkinson and Riani (2001) apply the forward search algorithm to deal with the problem of the detection of multiple outliers in binomial data. In this thesis, we extend the similar idea to identify multiple outliers for the generalized linear models when part of data are missing. The algorithm starts with imputation method to fill-in the missing observations in the data, and then use the forward search algorithm to confirm outliers. The proposed method can overcome the masking effect, which commonly occurs when multiple outliers exit in the data. Real data are used to illustrate the procedure, and satisfactory results are obtained.

The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the "classical" approach and the "inverse" regression approach. Both of these models are static models and are used to estimate "exact" measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe the measurement. The Bayesian time series analysis method of Dynamic Linear Models (DLM) can be used to monitor the evolution of the measures, thus introducing a dynamic approach to statistical calibration. The research presented employs the use of Bayesian methodology to perform statistical calibration. The DLM framework is used to capture the time-varying parameters that may be changing or drifting over time. Dynamic based approaches to the linear, nonlinear, and multivariate calibration problem are presented in this dissertation. Simulation studies are conducted where the dynamic models are compared to some well known "static'" calibration approaches in the literature from both the frequentist and Bayesian perspectives. Applications to microwave radiometry are given.

Abstract In a two-level hierarchical linear model(HLM2), the outcome as well as covariates may have missing values at any of the levels. One way to analyze all available data in the model is to estimate a multivariate normal joint distribution of variables, including the outcome, subject to missingness conditional on covariates completely observed by maximum likelihood(ML); draw multiple imputation (MI) of missing values given the estimated joint model; and analyze the hierarchical model given the MI [1,2]. The assumption is data missing at random (MAR). While this method yields efficient estimation of the hierarchical model, it often estimates the model given discrete missing data that is handled under multivariate normality. In this thesis, we evaluate how robust it is to estimate a hierarchical linear model given discrete missing data by the method. We simulate incompletely observed data from a series of hierarchical linear models given discrete covariates MAR, estimate the models by the method, and assess the sensitivity of handling discrete missing data under the multivariate normal joint distribution by computing bias, root mean squared error, standard error, and coverage probability in the estimated hierarchical linear models via a series of simulation studies. We want to achieve the following aim: Evaluate the performance of the method handling binary covariates MAR. We let the missing patterns of level-1 and -2 binary covariates depend on completely observed variables and assess how the method handles binary missing data given different values of success probabilities and missing rates. Based on the simulation results, the missing data analysis is robust under certain parameter settings. Efficient analysis performs very well for estimation of level-1 fixed and random effects across varying success probabilities and missing rates. MAR estimation of level-2 binary covariate is not well estimated when the missing rate in level-2 binary covariate is greater than 10%. The rest of the thesis is organized as follows: Section 1 introduces the background information including conventional methods for hierarchical missing data analysis, different missing data mechanisms, and the innovation and significance of this study. Section 2 explains the efficient missing data method. Section 3 represents the sensitivity analysis of the missing data method and explain how we carry out the simulation study using SAS, software package HLM7, and R. Section 4 illustrates the results and useful recommendations for researchers who want to use the missing data method for binary covariates MAR in HLM2. Section 5 presents an illustrative analysis National Growth of Health Study (NGHS) by the missing data method. The thesis ends with a list of useful references that will guide the future study and simulation codes we used.

In this thesis we describe the theory of generalized linear models and demon- strate its applications in non-life insurance. We also introduce some methods com- monly used to estimation of regression parameters and hypothesis testing . Further- more, we discuss possible extensions of GLM by introducing tools for reparametriza- tion of predictors which leads to new classes of models, concretely to segmented generalized linear models and generalized additive models. Consequently, we derive models appropriate for actuarial praxis using the real insurance data. In practical part of this thesis we illustrate the use of appropriate software for calculating the parameters of GAM and find way how to use open source statistical program .

The aim of this diploma thesis is statistical processing of a sample of patients that have been hospitalized and treated for ureteropelvic junction obstruction at the urological department of ÚNV Prague in last 20 years and to determine the optimal treatment method. Evaluation of surgical techniques from the surgical and economical point of creates a comprehensive image of advantages and disadvantages connected with application of a particular method and enables all participating subjects to decide in case of doubt. In this case the statistical analysis is a proper instrument, leading to find answers, however, it also gives an opportunity for discussion.