This dissertation aims to develop methods for statistical predictions based on various types of data from different areas. We focus on applications from reliability and spatial epidemiology. Chapter 1 gives a general introduction of statistical predictions. Chapters 2 and 3 investigate the photodegradation of an organic coating, which is mainly caused by ultraviolet (UV) radiation but also affected by environmental factors, including temperature and humidity. In Chapter 2, we identify a physically motivated nonlinear mixed-effects model, including the effects of environmental variables, to describe the degradation path. Unit-to-unit variabilities are modeled as random effects. The maximum likelihood approach is used to estimate parameters based on the accelerated test data from laboratory. The developed model is then extended to allow for time-varying covariates and is used to predict outdoor degradation where the explanatory variables are time-varying. Chapter 3 introduces a class of models for analyzing degradation data with dynamic covariate information. We use a general path model with random effects to describe the degradation paths and a vector time series model to describe the covariate process. Shape restricted splines are used to estimate the effects of dynamic covariates on the degradation process. The unknown parameters of these models are estimated by using the maximum likelihood method. Algorithms for computing the estimated lifetime distribution are also described. The proposed methods are applied to predict the photodegradation path of an organic coating in a complicated dynamic environment. Chapter 4 investigates the Lyme disease emergency in Virginia at census tract level. Based on areal (census tract level) count data of Lyme disease cases in Virginia from 1998 to 2011, we analyze the spatial patterns of the disease using statistical smoothing techniques. We also use the space and space-time scan statistics to reveal the presence of clusters in the spatial and spatial/temporal distribution of Lyme disease. Chapter 5 builds a predictive model for Lyme disease based on historical data and environmental/demographical information of each census tract. We propose a Divide-Recombine method to take advantage of parallel computing. We compare prediction results through simulation studies, which show our method can provide comparable fitting and predicting accuracy but can achieve much more computational efficiency. We also apply the proposed method to analyze Virginia Lyme disease spatio-temporal data. Our method makes large-scale spatio-temporal predictions possible. Chapter 6 gives a general review on the contributions of this dissertation, and discusses directions for future research. / Ph. D.

<p dir="ltr">This dissertation addresses three progressively fundamental problems for functional data analysis: (1) To do efficient inference for the functional mean model accounting for within-subject correlation, we propose the refined and bias-corrected empirical likelihood method. (2) To identify functional subjects potentially from different populations, we propose the dominant-set based unsupervised clustering method using the similarity matrix. (3) To learn the similarity matrix from various similarity metrics for functional data clustering, we propose the modularity guided and dominant-set based semi-supervised clustering method.</p><p dir="ltr">In the first problem, the empirical likelihood method is utilized to do inference for the mean function of functional data by constructing the refined and bias-corrected estimating equation. The proposed estimating equation not only improves efficiency but also enables practically feasible empirical likelihood inference by properly incorporating within-subject correlation, which has not been achieved by previous studies.</p><p dir="ltr">In the second problem, the dominant-set based unsupervised clustering method is proposed to maximize the within-cluster similarity and applied to functional data with a flexible choice of similarity measures between curves. The proposed unsupervised clustering method is a hierarchical bipartition procedure under the penalized optimization framework with the tuning parameter selected by maximizing the clustering criterion called modularity of the resulting two clusters, which is inspired by the concept of dominant set in graph theory and solved by replicator dynamics in game theory. The advantage offered by this approach is not only robust to imbalanced sizes of groups but also to outliers, which overcomes the limitation of many existing clustering methods.</p><p dir="ltr">In the third problem, the metric-based semi-supervised clustering method is proposed with similarity metric learned by modularity maximization and followed by the above proposed dominant-set based clustering procedure. Under semi-supervised setting where some clustering memberships are known, the goal is to determine the best linear combination of candidate similarity metrics as the final metric to enhance the clustering performance. Besides the global metric-based algorithm, another algorithm is also proposed to learn individual metrics for each cluster, which permits overlapping membership for the clustering. This is innovatively different from many existing methods. This method is superiorly applicable to functional data with various similarity metrics between functional curves, while also exhibiting robustness to imbalanced sizes of groups, which are intrinsic to the dominant-set based clustering approach.</p><p dir="ltr">In all three problems, the advantages of the proposed methods are demonstrated through extensive empirical investigations using simulations as well as real data applications.</p>

L’objectif principal de cette thèse est de développer des méthodologies statistiques adaptées au traitement de données issues de processus stochastiques et plus précisément de processus de Cox.Les problématiques étudiées dans cette thèse sont issues des trois domaines statistiques suivants : les tests non paramétriques, l’estimation non paramétrique à noyaux et l’estimation minimax.Dans un premier temps, nous proposons, dans un cadre fonctionnel, des statistiques de test pour détecter la nature Poissonienne d’un processus de Cox.Nous étudions ensuite le problème de l’estimation minimax de la régression sur un processus de Poisson ponctuel. En se basant sur la décomposition en chaos d’Itô, nous obtenons des vitesses comparables à celles atteintes pour le cas de la régression Lipschitz en dimension finie.Enfin, dans le dernier chapitre de cette thèse, nous présentons un estimateur non-paramétrique de l’intensité d’un processus de Cox lorsque celle-ci est une fonction déterministe d’un co-processus. / The main purpose of this thesis is to develop statistical methodologies for stochastic processes data and more precisely Cox process data.The problems considered arise from three different contexts: nonparametric tests, nonparametric kernel estimation and minimax estimation.We first study the statistical test problem of detecting wether a Cox process is Poisson or not.Then, we introduce a semiparametric estimate of the regression over a Poisson point process. Using Itô’s famous chaos expansion for Poisson functionals, we derive asymptotic minimax properties of our estimator.Finally, we introduce a nonparametric estimate of the intensity of a Cox process whenever it is a deterministic function of a known coprocess.

In vielen Anwendungen ist es notwendig, die stochastische Schwankungen der maximalen Abweichungen der nichtparametrischen Schätzer von Quantil zu wissen, zB um die verschiedene parametrische Modelle zu überprüfen. Einheitliche Konfidenzbänder sind daher für nichtparametrische Quantil Schätzungen der Regressionsfunktionen gebaut. Die erste Methode basiert auf der starken Approximation der empirischen Verfahren und Extremwert-Theorie. Die starke gleichmäßige Konsistenz liegt auch unter allgemeinen Bedingungen etabliert. Die zweite Methode beruht auf der Bootstrap Resampling-Verfahren. Es ist bewiesen, dass die Bootstrap-Approximation eine wesentliche Verbesserung ergibt. Der Fall von mehrdimensionalen und diskrete Regressorvariablen wird mit Hilfe einer partiellen linearen Modell behandelt. Das Verfahren wird mithilfe der Arbeitsmarktanalysebeispiel erklärt. Hoch-dimensionale Zeitreihen, die nichtstationäre und eventuell periodische Verhalten zeigen, sind häufig in vielen Bereichen der Wissenschaft, zB Makroökonomie, Meteorologie, Medizin und Financial Engineering, getroffen. Der typische Modelierungsansatz ist die Modellierung von hochdimensionalen Zeitreihen in Zeit Ausbreitung der niedrig dimensionalen Zeitreihen und hoch-dimensionale zeitinvarianten Funktionen über dynamische Faktorenanalyse zu teilen. Wir schlagen ein zweistufiges Schätzverfahren. Im ersten Schritt entfernen wir den Langzeittrend der Zeitreihen durch Einbeziehung Zeitbasis von der Gruppe Lasso-Technik und wählen den Raumbasis mithilfe der funktionalen Hauptkomponentenanalyse aus. Wir zeigen die Eigenschaften dieser Schätzer unter den abhängigen Szenario. Im zweiten Schritt erhalten wir den trendbereinigten niedrig-dimensionalen stochastischen Prozess (stationär). / In many applications it is necessary to know the stochastic fluctuation of the maximal deviations of the nonparametric quantile estimates, e.g. for various parametric models check. Uniform confidence bands are therefore constructed for nonparametric quantile estimates of regression functions. The first method is based on the strong approximations of the empirical process and extreme value theory. The strong uniform consistency rate is also established under general conditions. The second method is based on the bootstrap resampling method. It is proved that the bootstrap approximation provides a substantial improvement. The case of multidimensional and discrete regressor variables is dealt with using a partial linear model. A labor market analysis is provided to illustrate the method. High dimensional time series which reveal nonstationary and possibly periodic behavior occur frequently in many fields of science, e.g. macroeconomics, meteorology, medicine and financial engineering. One of the common approach is to separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant functions via dynamic factor analysis. We propose a two-step estimation procedure. At the first step, we detrend the time series by incorporating time basis selected by the group Lasso-type technique and choose the space basis based on smoothed functional principal component analysis. We show properties of this estimator under the dependent scenario. At the second step, we obtain the detrended low dimensional stochastic process (stationary).

Dans cette thèse, nous étudions des modèles définis par des équations de moments conditionnels. Une grande partie de modèles statistiques (régressions, régressions quantiles, modèles de transformations, modèles à variables instrumentales, etc.) peuvent se définir sous cette forme. Nous nous intéressons au cas des modèles avec un paramètre à estimer de dimension finie, ainsi qu’au cas des modèles semi paramétriques nécessitant l’estimation d’un paramètre de dimension finie et d’un paramètre de dimension infinie. Dans la classe des modèles semi paramétriques étudiés, nous nous concentrons sur les modèles à direction révélatrice unique qui réalisent un compromis entre une modélisation paramétrique simple et précise, mais trop rigide et donc exposée à une erreur de modèle, et l’estimation non paramétrique, très flexible mais souffrant du fléau de la dimension. En particulier, nous étudions ces modèles semi paramétriques en présence de censure aléatoire. Le fil conducteur de notre étude est un contraste sous la forme d’une U-statistique, qui permet d’estimer les paramètres inconnus dans des modèles généraux. / In this dissertation we study statistical models defined by condition estimating equations. Many statistical models could be stated under this form (mean regression, quantile regression, transformation models, instrumental variable models, etc.). We consider models with finite dimensional unknown parameter, as well as semiparametric models involving an additional infinite dimensional parameter. In the latter case, we focus on single-index models that realize an appealing compromise between parametric specifications, simple and leading to accurate estimates, but too restrictive and likely misspecified, and the nonparametric approaches, flexible but suffering from the curse of dimensionality. In particular, we study the single-index models in the presence of random censoring. The guiding line of our study is a U-statistics which allows to estimate the unknown parameters in a wide spectrum of models.

This thesis is focused on creation of mobilization curves, based on data, obtained from standard and detailed monitoring of the load test. The load test was performed on the 9 meters long ductile micropile. The first part of the thesis explains the methods and principles, which was used to construct the mobilization curves. Next there is description of the technologies of ductile micropiles and the load test. In the next part of the thesis is generally explained process, which was applied to the evaluated data. For evaluation was used spreadsheet Microsoft Excel and programming language Matlab, with Kernel Smoothing extension. In the last chapter of the thesis there are interpreted the load transfer function together with skin friction and micropile displacement.