Doctor of Philosophy / Department of Statistics / Weixing Song / Kernel based non-parametric regression is a popular statistical tool to identify the relationship between response and predictor variables when standard parametric regression models are not appropriate. The efficacy of kernel based methods depend both on the kernel choice and the smoothing parameter. With insufficient smoothing, the resulting regression estimate is too rough and with excessive smoothing, important features of the underlying relationship is lost. While the choice of the kernel has been shown to have less of an effect on the quality of regression estimate, it is important to choose kernels to best match the support set of the underlying predictor variables. In the past few decades, there have been multiple efforts to quantify the properties of asymmetric kernel density and regression estimators. Unlike classic symmetric kernel based estimators, asymmetric kernels do not suffer from boundary problems. For example, Beta kernel estimates are especially suitable for investigating the distribution structure of predictor variables with compact support. In this dissertation, two types of Beta kernel based non parametric regression estimators are proposed and analyzed. First, a Nadaraya-Watson type Beta kernel estimator is introduced within the regression setup followed by a local linear regression estimator based on Beta kernels. For both these regression estimators, a comprehensive analysis of its large sample properties is presented. Specifically, for the first time, the asymptotic normality and the uniform almost sure convergence results for the new estimators are established. Additionally, general guidelines for bandwidth selection is provided. The finite sample performance of the proposed estimator is evaluated via both a simulation study and a real data application. The results presented and validated in this dissertation help advance the understanding and use of Beta kernel based methods in other non-parametric regression applications.

As rações comerciais devem ser um alimento balanceado que supra todas as exigências nutricionais nas diferentes fases da vida do animal. Sua formulação deve conter ingredientes de qualidade, em proporções adequadas. É de fundamental importância o conhecimento do valor nutricional das rações, para assegurar que o cão esteja ingerindo diariamente quantidades corretas dos nutrientes. O desbalanço de elementos essenciais e a presença de elementos tóxicos podem causar desequilíbrios nutricionais, doenças e, até mesmo, consequências fatais aos cães. O cobre é um dos vários elementos de importância a ser estudado quanto aos defeitos metabólicos nos cães. O acúmulo de cobre no fígado pode ocasionar lesões progressivas nas organelas dos hepatócitos, resultando em hepatite crônica e cirrose. Diante disso, este trabalho teve como objetivos (I) quantificação dos elementos químicos com função nutricional e com potencial tóxico presentes nas rações para cães adultos e filhotes, (II) avaliação da composição centesimal das rações amostradas, (III) avaliação da variação dos elementos químicos entre as amostras de ração de um mesmo lote de produção (IV), estudo da representatividade de pequenas porções-teste, (V) avaliação da bioacessibilidade de cobre em rações, com experimento in vitro. Os elementos químicos Al, As, Br, Ca, Cl, Co, Cr, Cs, Cu, Fe, I, K, La, Mg, Mn, Na, P, Rb, Sb, Sc, Se, Ti, U e Zn foram determinados pela análise por ativação neutrônica instrumental (INAA). A composição centesimal foi avaliada de acordo com os métodos recomendados da AOAC. A homogeneidade de distribuição dos elementos químicos nas rações foi avaliada pela análise de amostras grandes (LS-NAA). A bioacessibilidade de cobre nas rações foi estimada por meio da simulação da digestão gastrointestinal in vitro. Foi possível determinar por INAA todos os nutrientes minerais, isto é, Ca, P, K, Na, Cl, Mg, Fe, Cu, Mn, Zn, I e Se, com limites estabelecidos pela Association of American Feed Control Officials. Foram notadas em algumas rações altas concentrações de Al, Sb e U, elementos com grande potencial tóxico. Cerca de 16 % das amostras de ração apresentaram, pelo menos, um parâmetro não conforme quanto à composição centesimal. Os resultados obtidos por LS-NAA e NAA convencional mostraram variação na composição entre os sacos de ração para Br, Ca, Na e Zn, com boa concordância entre ambos os métodos. O emprego da LS-NAA combinada com NAA convencional permitiu observar que pequenas porções-teste (350 mg) de ração são representativas comparadas com aquelas de 1 kg para Br, Ca, K, Na e Zn. Em todas as rações para cães, 50 % do cobre presente estava sob a forma bioacessível / Commercial dog foods should be a balanced diet that meets all nutritional requirements at different stages of the animal\'s life. Its formulation should contain quality ingredients in suitable proportions. The knowledge of the nutritional value of dog food is fundamental to ensure that the animal is ingesting daily right amounts of nutrients. The imbalance of essential elements and the presence of toxic elements can cause nutritional problems, diseases, and even fatal consequences for dogs. Copper is one of several important factors to be studied for metabolic defects in dogs. Copper accumulation in the liver may cause progressive lesions in the organelles of hepatocytes, resulting in chronic hepatitis and cirrhosis. Thus, this study aimed to (I) determine essential and potentially toxic chemical elements in the dog food for puppies and adults, (II) assess the proximate composition of the sampled dog food, (III) evaluate the between-bag variation of chemical elements in dog food within the same production lot of one brand, (IV) study the representativeness of small test portions of dog food collected from regular 1 kg packed bags, (V) assess the in vitro bioaccessibility of copper in dog food. The chemical elements Al, As, Br, Ca, Cl, Co, Cr, Cs, Cu, Fe, I, K, La, Mg, Mn, Na, P, Rb, Sb, Sc, Se, Ti, U and Zn were determined by instrumental neutron activation analysis (INAA). The proximate composition was evaluated by AOAC recommended methods. The homogeneity of chemical elements distribution in the dog food was evaluated by analysis of large samples (LS-NAA). The bioaccessibility of copper was estimated by in vitro simulated gastrointestinal digestion. INAA was a suitable analytical tool for characterizing the profile of mineral nutrients, i.e., Ca, P, K, Na, Cl, Mg, Fe, Cu, Mn, Zn, I and Se in dog food with reference values set by Association of American Feed Control Officials. High concentrations of the toxic elements Al, Sb and U were observed in some dog food samples. Approximately 16% of dog food samples presented, at least, one value outside the reference limits from proximate composition. The results obtained by LS-NAA and conventional NAA showed between-bag compositional variability for Br, Ca, Na and Zn, with a good agreement between both methods. The use of LS NAA combined with conventional NAA allowed to observe that the small 350 mg portions of dry dog food taken for analysis is representative of one kilogram bag for Br, Ca, K, Na and Zn. In all dog foods, 50 % of the copper was present in bioaccessible form

As rações comerciais devem ser um alimento balanceado que supra todas as exigências nutricionais nas diferentes fases da vida do animal. Sua formulação deve conter ingredientes de qualidade, em proporções adequadas. É de fundamental importância o conhecimento do valor nutricional das rações, para assegurar que o cão esteja ingerindo diariamente quantidades corretas dos nutrientes. O desbalanço de elementos essenciais e a presença de elementos tóxicos podem causar desequilíbrios nutricionais, doenças e, até mesmo, consequências fatais aos cães. O cobre é um dos vários elementos de importância a ser estudado quanto aos defeitos metabólicos nos cães. O acúmulo de cobre no fígado pode ocasionar lesões progressivas nas organelas dos hepatócitos, resultando em hepatite crônica e cirrose. Diante disso, este trabalho teve como objetivos (I) quantificação dos elementos químicos com função nutricional e com potencial tóxico presentes nas rações para cães adultos e filhotes, (II) avaliação da composição centesimal das rações amostradas, (III) avaliação da variação dos elementos químicos entre as amostras de ração de um mesmo lote de produção (IV), estudo da representatividade de pequenas porções-teste, (V) avaliação da bioacessibilidade de cobre em rações, com experimento in vitro. Os elementos químicos Al, As, Br, Ca, Cl, Co, Cr, Cs, Cu, Fe, I, K, La, Mg, Mn, Na, P, Rb, Sb, Sc, Se, Ti, U e Zn foram determinados pela análise por ativação neutrônica instrumental (INAA). A composição centesimal foi avaliada de acordo com os métodos recomendados da AOAC. A homogeneidade de distribuição dos elementos químicos nas rações foi avaliada pela análise de amostras grandes (LS-NAA). A bioacessibilidade de cobre nas rações foi estimada por meio da simulação da digestão gastrointestinal in vitro. Foi possível determinar por INAA todos os nutrientes minerais, isto é, Ca, P, K, Na, Cl, Mg, Fe, Cu, Mn, Zn, I e Se, com limites estabelecidos pela Association of American Feed Control Officials. Foram notadas em algumas rações altas concentrações de Al, Sb e U, elementos com grande potencial tóxico. Cerca de 16 % das amostras de ração apresentaram, pelo menos, um parâmetro não conforme quanto à composição centesimal. Os resultados obtidos por LS-NAA e NAA convencional mostraram variação na composição entre os sacos de ração para Br, Ca, Na e Zn, com boa concordância entre ambos os métodos. O emprego da LS-NAA combinada com NAA convencional permitiu observar que pequenas porções-teste (350 mg) de ração são representativas comparadas com aquelas de 1 kg para Br, Ca, K, Na e Zn. Em todas as rações para cães, 50 % do cobre presente estava sob a forma bioacessível / Commercial dog foods should be a balanced diet that meets all nutritional requirements at different stages of the animal\'s life. Its formulation should contain quality ingredients in suitable proportions. The knowledge of the nutritional value of dog food is fundamental to ensure that the animal is ingesting daily right amounts of nutrients. The imbalance of essential elements and the presence of toxic elements can cause nutritional problems, diseases, and even fatal consequences for dogs. Copper is one of several important factors to be studied for metabolic defects in dogs. Copper accumulation in the liver may cause progressive lesions in the organelles of hepatocytes, resulting in chronic hepatitis and cirrhosis. Thus, this study aimed to (I) determine essential and potentially toxic chemical elements in the dog food for puppies and adults, (II) assess the proximate composition of the sampled dog food, (III) evaluate the between-bag variation of chemical elements in dog food within the same production lot of one brand, (IV) study the representativeness of small test portions of dog food collected from regular 1 kg packed bags, (V) assess the in vitro bioaccessibility of copper in dog food. The chemical elements Al, As, Br, Ca, Cl, Co, Cr, Cs, Cu, Fe, I, K, La, Mg, Mn, Na, P, Rb, Sb, Sc, Se, Ti, U and Zn were determined by instrumental neutron activation analysis (INAA). The proximate composition was evaluated by AOAC recommended methods. The homogeneity of chemical elements distribution in the dog food was evaluated by analysis of large samples (LS-NAA). The bioaccessibility of copper was estimated by in vitro simulated gastrointestinal digestion. INAA was a suitable analytical tool for characterizing the profile of mineral nutrients, i.e., Ca, P, K, Na, Cl, Mg, Fe, Cu, Mn, Zn, I and Se in dog food with reference values set by Association of American Feed Control Officials. High concentrations of the toxic elements Al, Sb and U were observed in some dog food samples. Approximately 16% of dog food samples presented, at least, one value outside the reference limits from proximate composition. The results obtained by LS-NAA and conventional NAA showed between-bag compositional variability for Br, Ca, Na and Zn, with a good agreement between both methods. The use of LS NAA combined with conventional NAA allowed to observe that the small 350 mg portions of dry dog food taken for analysis is representative of one kilogram bag for Br, Ca, K, Na and Zn. In all dog foods, 50 % of the copper was present in bioaccessible form

In this paper we consider the problem of constructing confidence intervals and lower bounds forthe intraclass correlation coefficient in an interrater reliability study where the raters are randomly selected from a population of raters.The likelihood function of the interrater reliability is derived and simplified, and the profile likelihood based approach is readily available for computing the confidence intervals of the interrater reliability. Unfortunately, the confidence intervals computed by using the profile likelihood function are in general too narrow to have the desired coverage probabilities. From the point view of practice, a conservative approach, if is at least as precise as any existing method, is preferred sinceit gives the correct results with a probability higher than claimed. Under this rationale, we propose the so-called modified likelihood approach in this paper. Simulation study shows that, the proposed method in general has better performance than currently used methods.

The purpose of this study was to investigate the relationship between cigarette smoking and socio-demographic variables based on the empirical literature and the primitive theories in the field. Two regression approaches, logistic regression and linear multiple regression, were conducted on the two most recent Arizona Adult Tobacco Surveys to test the hypothesized models. The results showed that cigarette smokers in Arizona are mainly residents who have not completed a four-year college degree, who are unemployed, White, non-Hispanic, or young to middle-aged adults. Among the socio-demographic predictors of interest, education is the most important variable in identifying cigarette smokers, even though the predictive power of these socio-demographic variables is small. Practical and methodological implications of these findings are discussed.

acase@tulane.edu

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