Functional data analysis (FDA) has grown into a substantial field of statistical research, with new methodology, numerous useful applications and interesting novel theoretical developments. My dissertation focuses on the empirical properties of functional regression models and their application to financial data. We start from testing the empirical properties of forecasts with the functional autoregressive models based on simulated and real data. We define intraday returns and consider their prediction from such returns on a market index. This is an extension to intraday data of the Capital Asset Pricing model. Finally we investigate multifactor functional models and assess their suitability for the prediction of intraday returns for various financial assets, including stock and commodity futures.

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Within the realms of biological and medical research, toxicity studies which measure impaired reproduction are becoming more and more common, yet methods for efficiently designing experiments for these studies have received little attention. In this research, response surface design criteria are applied to four models for impaired reproduction data. The important role of control observations in impairment studies is discussed, and for one model, a normal error linear model, a design criterion is introduced for allocating a portion of the sample to the control. Special attention is focused on issues surrounding optimal design of experiments for two of the models, a Poisson exponential model and a Poisson linear model. As most of the optimal designs for these models are obtained via numerical methods rather than directly from criteria, equivalence theory is used to prove analytically that the numerically obtained designs are truly optimal. A further complication associated with designing experiments for Poisson regression is the need to know parameter values in order to implement the optimal designs. Thus, two stage design of experiments is investigated as one solution to this problem. Finally, since researchers frequently do not know the appropriate model for their data a priori, the optimal designs for these two different models are compared, and designs which are robust to model misspecification are highlighted. / Ph. D.

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This thesis investigates how three different machine learning models perform on cardinalty estimation for sql queries. All three models were evaluated on three different data sets. The models were tested on both estimating cardinalities when the query just takes information from one table and also a two way join case. Postgresql's own cardinality estimator was used as a baseline. The evaluated models were: Artificial neural networks, random forests and extreme gradient boosted trees. What was found is that the model that performs best is the extreme gradient boosted tree with a tweedie regression loss function. To the authors knowledge, this is the first time an extreme gradient boosted tree has been used in this context. / Denna uppsats undersöker hur tre olika maskininlärningsmodeller presterar på kardinalitetsuppskattning för sql förfrågningar till en databas. Alla tre modeller utvärderades på tre olika datauppsättningar. Modellerna fick både behandla förfrågningar från en tabell, samt en sammanslagning mellan två tabeller. Postgresql's egna kardinalitetsestimerare användes som referenspunkt. De utvärderade modellerna var följande: artificiella neurala nätverk, random forests och extreme gradient boosted trees. En slutsats var att den modellen som utförde uppgiften bäst var extreme gradient boosted trees med en tweedie-regression förlustfunktion. Såvitt författaren vet är det här första gången den här typen av extreme gradient boosted tree används på denna typ av problem.

The focus of this dissertation is the theory of qualitative response models and its application to forestry related problems. Qualitative response models constitute a class of regression models used for predicting the result in one of a discrete number of mutually exclusive outcomes. These models, also known as discrete regression models, differ from the usual continuous regression models in that the response variable takes only discrete values. In forestry applications the use of such models has been largely confirmed to mortality studies where only the simplest kind of qualitative response models - a dichotomous (binary) dependent variable model - is applied. However, it is common in forestry to deal with many variables which are either discrete or recorded discretely and need to be formulated by more complex models involving polychotomous dependent variables. The estimation of such complex qualitative response models only recently has been made possible by the development of advanced computer technology. The first objective of this study was to specify dichotomous and polychotomous response models that appear to be suitable for forestry applications and present methods of statistical analysis for these models. The models considered in this study were: the linear probability model, binary logit and probit, ordered and unordered multinomiallogit and probit and McFadden's conditionallogit. Special attention was paid to the following problems: i) how to motivate a qualitative response model which is theoretically correct and statistically manageable, ii) how to estimate and draw inferences about the model parameters, iii) what criteria to use when choosing among competing models and iv) how to detect outlying, high leverage and highly influential observations. The second objective was to exemplify the utility of the above models by considering two, forestry related, case studies. Assessing the merchantability of loblolly pine trees growing on plantations in southern United States and modelling the incidence and spread of fusifonn rust on loblolly and slash pine plantations in east Texas. The results demonstrated the potential of qualitative response models for meaningful implementation in a variety of forestry applications and also, suggested topics for future research work. / Ph. D.

Em modelos de regressão em que uma covariável é medida com erro, é comum o uso de estruturas que relacionam a covariável observada com a verdadeira covariável não observada. Essas estruturas são usualmente aditivas ou multiplicativas. Na literatura existem diversos trabalhos interessantes que tratam de modelos de regressão com erro de medida aditivo, muitos dos quais são modelos lineares com covariáveis e erro de medida normalmente distribuídos. Para modelos em que o erro de medida é multipicativo, não se encontra na literatura o mesmo desenvolvimento teórico encontrado para modelos em que o erro de medida é aditivo. O mesmo vale para situações em que as suposições de normalidade para as covariáveis e erro de medida não se aplicam. Este trabalho propõe a construção, definição, métodos de estimação e análise de diagnóstico para modelos de regressão com erro de medida multiplicativo em uma das covariáveis. Para esses modelos, consideramos que a variável resposta possa pertencer ou à classe de modelos de regressão série de potências modificadas ou à família exponencial. O rol de distribuições pertencentes à família série de potências modificada é bem abrangente, portanto, neste trabalho, desenvolvemos a teoria de estimação e validação do modelo primeiramente de forma geral e, para exemplificar, apresentamos o modelo de regressão binomial negativa com erro de medida. para o caso em que a variável resposta pertença à família exponencial. apresentamos o modelo de regressão beta com erro de medida multiplicativo. Todos os modelos propostos foram analisados através de estados de simulação e aplicados a conjuntos de dados reais. / In regression models in which a covariate is measured with erros, it is common to use structures that correlate the observed covariate with the true non-observed covariate. Such structures are usually additive or multiplicative. In the literatue there are several interesting works that deal with regression models having an additive measuremsnt error, many of which are linear models with covariate and measurement error normally distributed. For models having a multiplicative measurement error, one does not find in the literature the same theoretical amount of works as one finds for models in which the measurement error is additive. The same happens in situations where the supositions of normality for the covariates and the measurement errors do not apply. The presente work proposes the construction,definition, estimation methods, and diagnostic analysis for the regression models with a multiplicative measurement error in one of the covariates. For these models it is considered that the response variable may belong either to the class of modified power series regression models or to the exponential family. The list of distributions belonging to the family modified power series is rather comprehensive; for this reason this work develops, firstly and in a general way, the models estimation and validation theory, and, as an example, presents the model of negative binomial regression with measurement error. In the case where response variable belongs to the exponential family, the model of beta regression with multiplicative measurement error is presented. All proposed models were analysed through simulationb studies and applied to real data sets.

Submitted by Livia Mello (liviacmello@yahoo.com.br) on 2016-09-23T19:10:12Z No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:48:37Z (GMT) No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:48:44Z (GMT) No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) / Made available in DSpace on 2016-10-10T14:48:50Z (GMT). No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) Previous issue date: 2016-02-04 / Não recebi financiamento / In regression models in which a covariate is measured with error, it is common to use structures that correlate the observed covariate with the true non-observed covariate. Such structures are usually additive or multiplicative. In the literature there are several interesting works that deal with regression models having an additive measurement error, many of which are linear models with covariate and measurement error normally distributed. For models having a multiplicative measurement error, one does not find in the literature the same theoretical amount of works as one finds for models in which the measurement error is additive. The same happens in situations where the supositions of normality for the covariates and the measurement errors do not apply. The present work proposes the construction, definition, estimation methods, and diagnostic analysis for the regression models with a multiplicative measurement error in one of the covariates. For these models it is considered that the response variable may belong either to the class of modified power series regression models or to the exponential family. The list of distributions belonging to the family modified power series is rather comprehensive; for this reason this work develops, firstly and in a general way, the models estimation and validation theory, and, as an example, presents the model of negative binomial regression with measurement error. In the case where the response variable belongs to the exponential family, the model of beta regression with multiplicative measurement error is presented. All proposed models were analysed through simulation studies and applied to real data sets. / Em modelos de regressão em que uma covariável é medida com erro, é comum o uso de estruturas que relacionam a covariável observada com a verdadeira covariável não observada. Essas estruturas são usualmente aditivas ou multiplicativas. Na literatura existem diversos trabalhos interessantes que tratam de modelos de regressão com erro de medida aditivo, muitos dos quais são modelos lineares com covariáveis e erro de medida normalmente distribuídos. Para modelos em que o erro de medida é multiplicativo, não se encontra na literatura o mesmo desenvolvimento teórico encontrado para modelos em que o erro de medida é aditivo. O mesmo vale para situações em que as suposições de normalidade para as covariáveis e erro de medida não se aplicam. Este trabalho propõe a construção, definição, métodos de estimação e análise de diagnóstico para modelos de regressão com erro de medida multiplicativo em uma das covariáveis. Para esses modelos, consideramos que a variável resposta possa pertencer ou à classe de modelos de regressão série de potências modificadas ou à família exponencial. O rol de distribuições pertencentes à família série de potências modificada é bem abrangente, portanto, neste trabalho, desenvolvemos a teoria de estimação e validação do modelo primeiramente de forma geral e, para exemplificar, apresentamos o modelo de regressão binomial negativa com erro de medida. Para o caso em que a variável resposta pertença à família exponencial, apresentamos o modelo de regressão beta com erro de medida multiplicativo. Todos os modelos propostos foram analisados através de estudos de simulação e aplicados a conjuntos de dados reais.

Spatial-temporal autologistic models are useful models for binary data that are measured repeatedly over time on a spatial lattice. They can account for effects of potential covariates and spatial-temporal statistical dependence among the data. However, the traditional parametrization of spatial-temporal autologistic model presents difficulties in interpreting model parameters across varying levels of statistical dependence, where its non-negative autocovariates could bias the realizations toward 1. In order to achieve interpretable parameters, a centered spatial-temporal autologistic regression model has been developed. Two efficient statistical inference approaches, expectation-maximization pseudo-likelihood approach (EMPL) and Monte Carlo expectation-maximization likelihood approach (MCEML), have been proposed. Also, Bayesian inference is considered and studied. Moreover, the performance and efficiency of these three inference approaches across various sizes of sampling lattices and numbers of sampling time points through both simulation study and a real data example have been studied. In addition, We consider the imputation of missing values is for spatial-temporal autologistic regression models. Most existing imputation methods are not admissible to impute spatial-temporal missing values, because they can disrupt the inherent structure of the data and lead to a serious bias during the inference or computing efficient issue. Two imputation methods, iteration-KNN imputation and maximum entropy imputation, are proposed, both of them are relatively simple and can yield reasonable results. In summary, the main contributions of this dissertation are the development of a spatial-temporal autologistic regression model with centered parameterization, and proposal of EMPL, MCEML, and Bayesian inference to obtain the estimations of model parameters. Also, iteration-KNN and maximum entropy imputation methods have been presented for spatial-temporal missing data, which generate reliable imputed values with the reasonable efficient imputation time.