Binomial AR(1) process is a model for integer-valued time series with a fi- nite range and discrete time. It has the binomial marginal distribution and the AR(1)-like autocorrelation structure. This thesis deals with deriving some ba- sic properties of this process, methods of parameter estimation and goodness of fit testing. Three methods of parameter estimation are presented: Yule-Walker, the conditional least squares and the maximum likelihood method together with proofs of their asymptotical properties. Next, the goodness of fit testing is pre- sented. At first, two known methods based on the marginal distribution and the autocorrelation function are summarized. Then our own method is added, based on the probability generating function. Several simulations are provided to show the properties of all tests. The application of this model is illustrated on a real dataset. 1

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Notre progiciel PoweR vise à faciliter l'obtention ou la vérification des études empiriques de puissance pour les tests d'ajustement. En tant que tel, il peut être considéré comme un outil de calcul de recherche reproductible, car il devient très facile à reproduire (ou détecter les erreurs) des résultats de simulation déjà publiés dans la littérature. En utilisant notre progiciel, il devient facile de concevoir de nouvelles études de simulation. Les valeurs critiques et puissances de nombreuses statistiques de tests sous une grande variété de distributions alternatives sont obtenues très rapidement et avec précision en utilisant un C/C++ et R environnement. On peut même compter sur le progiciel snow de R pour le calcul parallèle, en utilisant un processeur multicœur. Les résultats peuvent être affichés en utilisant des tables latex ou des graphiques spécialisés, qui peuvent être incorporés directement dans vos publications. Ce document donne un aperçu des principaux objectifs et les principes de conception ainsi que les stratégies d'adaptation et d'extension. / Package PoweR aims at facilitating the obtainment or verification of empirical power studies for goodness-of-fit tests. As such, it can be seen as a reproducible research computational tool because it becomes very easy to reproduce (or detect errors in) simulation results already published in the literature. Using our package, it becomes easy to design new simulation studies. The empirical levels and powers for many statistical test statistics under a wide variety of alternative distributions are obtained fastly and accurately using a C/C++ and R environment. One can even rely on package snow to parallelize their computations, using a multicore processor. The results can be displayed using LaTeX tables or specialized graphs, which can be directly incorporated into your publications. This paper gives an overview of the main design aims and principles as well as strategies for adaptation and extension. Hand-on illustrations are presented to get new users started easily.

In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1

V předložené práci se zabýváme problematikou stochastického modelování úro- kových sazeb. Jedním z nejobvyklejších postup· je modelovat dynamiku úroko- vých sazeb pomocí stochastické diferenciální rovnice difúze, jejímiž základními kameny jsou funkce driftu a funkce difúze. Od 70. let 20. století byla navržena celá řada model· tohoto typu, a ačkoli se tyto modely neustále zdokonalují, vyvstává přirozená otázka, zda se historicky pozorované úrokové sazby skutečně takovými difúzními rovnicemi řídily. V této práci budeme právě uvedenou hypo- tézu testovat pro několik nejběžnějších jednofaktorových model· úrokové sazby první generace. Z historických dat odhadneme obecnou momentovou metodou a metodou maximální věrohodnosti parametry jednotlivých difúzních rovnic a následně provedeme statistické testy dobré shody proložení těchto rovnic pozo- rovanými daty. 1

Data from insect studies may present different features. Univariate responses may be analyzed using generalized linear models (continuous and discrete data), survival models (time until event data), mixed effects models (longitudinal data), among other methods. These models may be used to analyse data from experiments which assess complex ecological processes, such as competition and predation. In that sense, computational tools are useful for researchers in several fields, e.g., insect biology and physiology, applied ecology and biological control. Using different datasets from entomology as motivation, as well as other types of datasets for illustration purposes, this work intended to develop new modelling frameworks and goodness-of-fit assessment tools. We propose accelerated failure rate mixed models with simultaneous location and scale modelling with regressors to analyse time-until-attack data from a choice test experiment. We use the exponential, Weibull and exponentiated-Weibull models, and assess goodness-of-fit using half-normal plots with simulation envelopes. These plots are the subject of an entire Chapter on an R package, called hnp, developed to implement them. We use datasets from different types of experiments to illustrate the use of these plots and the package. A bivariate extension to the N-mixture modelling framework is proposed to analyse longitudinal count data for two species from the same food web that may interact directly or indirectly, and example datasets from ecological studies are used. An advantage of this modelling framework is the computation of an asymmetric correlation coefficient, which may be used by ecologists to study the degree of association between species. The jointNmix R package was also developed to implement the estimation process for these models. Finally, we propose a goodness-of-fit assessment tool for bivariate models, analogous to the half-normal plot with a simulation envelope, and illustrate the approach with simulated data and insect competition data. This tool is also implemented in an R package, called bivrp. All software developed in this thesis is made available freely on the Comprehensive R Archive Network. / Dados provenientes de estudos com insetos podem apresentar características diferentes. Respostas univariadas podem ser analisadas utilizando-se modelos lineares generalizados (dados contínuos e discretos), modelos de análise de sobrevivência (dados de tempo até ocorrência de um evento), modelos de efeitos mistos (dados longitudinais), dentre outros métodos. Esses modelos podem ser usados para analisar dados provenientes de experimentos que avaliam processos ecológicos complexos, como competição e predação. Nesse sentido, ferramentas computacionais são úteis para pesquisadores em diversos campos, por exemplo, biologia e fisiologia de insetos, ecologia aplicada e controle biológico. Utilizando diferentes conjuntos de dados entomológicos como motivação, assim como outros tipos de dados para ilustrar os métodos, este trabalho teve como objetivos desenvolver novos modelos e ferramentas para avaliar a qualidade do ajuste. Foram propostos modelos de tempo de vida acelerado mistos, com modelagem simultânea dos parâmetros de locação e de escala com regressores, para analisar dados de tempo até ataque de um experimento que avaliou escolha de predadores. Foram utilizados modelos exponencial, Weibull e Weibull-exponenciado, e a qualidade do ajuste foi avaliada utilizando gráficos meio-normais com envelope de simulação. Esses gráficos são o assunto de um Capítulo inteiro sobre um pacote para o software R, chamado hnp, desenvolvido para implementá-los. Foram utilizados conjuntos de dados de diferentes tipos de experimentos para ilustrar o uso desses gráficos e do pacote. Uma extensão bivariada para os modelos chamados \"N-mixture\" foi proposta para analisar dados longitudinais de contagem para duas espécies pertencentes à mesma teia trófica, que podem interagir direta e indiretamente, e conjuntos de dados provenientes de estudos ecológicos são usados para ilustrar a abordagem. Uma vantagem dessa estratégica de modelagem é a obtenção de um coeficiente de correlação assimétrico, que pode ser utilizado por ecologistas para inferir acerca do grau de associação entre espécies. O pacote jointNmix foi desenvolvido para implemetar o processo de estimação para esses modelos. Finalmente, foi proposta uma ferramenta de avaliação de qualidade do ajuste para modelos bivariados, análoga ao gráfico meio-normal com envelope de simulação, e a metodologia _e ilustrada com dados simulados e dados de competição de insetos. Essa ferramenta está também implementada em um pacote para o R, chamado bivrp. Todo o software desenvolvido nesta tese está disponível, gratuitamente, na Comprehensive R Archive Network (CRAN).

In this paper we study parameter estimation via the Expectation Maximization (EM) algorithm for a continuous-time hidden Markov model with diffusion and point process observation. Inference problems of this type arise for instance in credit risk modelling. A key step in the application of the EM algorithm is the derivation of finite-dimensional filters for the quantities that are needed in the E-Step of the algorithm. In this context we obtain exact, unnormalized and robust filters, and we discuss their numerical implementation. Moreover, we propose several goodness-of-fit tests for hidden Markov models with Gaussian noise and point process observation. We run an extensive simulation study to test speed and accuracy of our methodology. The paper closes with an application to credit risk: we estimate the parameters of a hidden Markov model for credit quality where the observations consist of rating transitions and credit spreads for US corporations.

Under item response theory, three types of limited information goodness-of-fit test statistics – M2, Mord, and C2 – have been proposed to assess model-data fit when data are sparse. However, the evaluation of the performance of these GOF statistics under multidimensional item response theory (MIRT) models with polytomous data is limited. The current study showed that M2 and C2 were well-calibrated under true model conditions and were powerful under misspecified model conditions. Mord were not well-calibrated when the number of response categories was more than three. RMSEA2 and RMSEAC2 are good tools to evaluate approximate fit. The second study aimed to evaluate the psychometric properties of the Religious Commitment Inventory-10 (RCI-10; Worthington et al., 2003) within the IRT framework and estimate C2 and its RMSEA to assess global model-fit. Results showed that the RCI-10 was best represented by a bifactor model. The scores from the RCI-10 could be scored as unidimensional notwithstanding the presence of multidimensionality. Two-factor correlational solution should not be used. Study two also showed that religious commitment is a risk factor of intimate partner violence, whereas spirituality was a protecting factor from the violence. More alcohol was related with more abusive behaviors. Implications of the two studies were discussed.

在處理列聯表時，適合度檢定的結果如果是顯著的話，則意味著配適的模式並不恰當，這其中一個可能的原因是資料中存在離群細格．因此我們希望能夠針對問題癥結所在，找出離群細格，使得我們的資料可以利用一個比較簡單且容易解釋的模式來做分析．在這篇論文中，我們主要依據施苑玉[1995]所提出的方法作些許的改變，使得改進後的方法可以適用於三維列聯表的所有情形．此外我們也將 Simonoff 在1988年所提出的方法，以及 BMDP 統計軟體的程序 4F ，與我們所提出的方法相比較．由模擬實驗的結果可發現我們的方法比前述兩種方法更具可行性． / When fitting a loglinear model to a contingency table, a significant goodness-of-fit can be resulted because of the existence of a few outlyingcells. Since a simpler model is easier to interpret and conveys more easilyunderstood information about a table than a complicated one, we would liketo identify those outliers so that a simpler model would fit a given data set. In this research, a modification of Shih's [1995] procedure is provided, and the revised method is now applicable to any type of models related tothree-way tables. Some data sets are simulated to compare outliers detectedusing procedures proposed by Simonoff [1988], and BMDP program 4F with our proposed method. Based on the results through simulation, our revised procedure outperforms the other two procedures most of the time.