In this dissertation, I focus on the development and application of nonparametric methods in econometrics. First, a constrained nonparametric regression method is developed to estimate a function and its derivatives subject to shape restrictions implied by economic theory. The constrained estimators can be viewed as a set of empirical likelihood-based reweighted local polynomial estimators. They are shown to be weakly consistent and have the same first order asymptotic distribution as the unconstrained estimators. When the shape restrictions are correctly specified, the constrained estimators can achieve a large degree of finite sample bias reduction and thus outperform the unconstrained estimators. The constrained nonparametric regression method is applied on the estimation of daily option pricing function and state-price density function. Second, a modified Cumulative Sum of Squares (CUSQ) test is proposed to test structural changes in the unconditional volatility in a time-varying coefficient model. The proposed test is based on nonparametric residuals from local linear estimation of the time-varying coefficients. Asymptotic theory is provided to show that the new CUSQ test has standard null distribution and diverges at standard rate under the alternatives. Compared with a test based on least squares residuals, the new test enjoys correct size and good power properties. This is because, by estimating the model nonparametrically, one can circumvent the size distortion from potential structural changes in the mean. Empirical results from both simulation experiments and real data applications are presented to demonstrate the test's size and power properties. Third, an empirical study of testing the Purchasing Power Parity (PPP) hypothesis is conducted in a functional-coefficient cointegration model, which is consistent with equilibrium models of exchange rate determination with the presence of trans- actions costs in international trade. Supporting evidence of PPP is found in the recent float exchange rate era. The cointegration relation of nominal exchange rate and price levels varies conditioning on the real exchange rate volatility. The cointegration coefficients are more stable and numerically near the value implied by PPP theory when the real exchange rate volatility is relatively lower.

O objetivo deste trabalho é investigar o desempenho de estimadores baseados em momentos das famílias verossimilhança empírica generalizada (GEL) e mínimo contraste generalizado (GMC) na estimação de modelos de equilíbrio geral dinâmico e estocástico (DSGE), com enfoque na análise de robustez sob má-especificação, recorrente neste tipo de modelo. Como benchmark utilizamos método do momentos generalizado (GMM), máxima verossimilhança (ML) e inferência bayesiana (BI). Trabalhamos com um modelo de ciclos reais de negócios (RBC) que pode ser considerado o núcleo de modelos DSGE, apresenta dificuldades similares e facilita a análise dos resultados devido ao menor número de parâmetros. Verificamos por meio de experimentos de Monte Carlo se os estimadores estudados entregam resultados satisfatórios em termos de média, mediana, viés, erro quadrático médio, erro absoluto médio e verificamos a distribuição das estimativas geradas por cada estimador. Dentre os principais resultados estão: (i) o estimador verossimilhança empírica (EL) - assim como sua versão com condições de momento suavizadas (SEL) - e a inferência bayesiana (BI) foram, nesta ordem, os que obtiveram os melhores desempenhos, inclusive nos casos de especificação incorreta; (ii) os estimadores continous updating empirical likelihood (CUE), mínima distância de Hellinger (HD), exponential tilting (ET) e suas versões suavizadas apresentaram desempenho comparativo intermediário; (iii) o desempenho dos estimadores exponentially tilted empirical likelihood (ETEL), exponential tilting Hellinger distance (ETHD) e suas versões suavizadas foi bastante comprometido pela ocorrência de estimativas atípicas; (iv) as versões com e sem suavização das condições de momento dos estimadores das famílias GEL/GMC apresentaram desempenhos muito similares; (v) os estimadores GMM, principalmente no caso sobreidentificado, e ML apresentaram desempenhos consideravelmente abaixo de boa parte de seus concorrentes / The objective of this work is to investigate the performance of moment-based estimators of the generalized empirical likelihood (GEL) and generalized minimum contrast (GMC) families in the estimation of dynamic stochastic general equilibrium (DSGE) models, focusing on the robustness analysis under misspecification, recurrent in this model. As benchmark we used generalized method of moments (GMM), maximum likelihood (ML) and Bayesian inference (BI). We work with a real business cycle (RBC) model that can be considered the core of DSGE models, presents similar difficulties and facilitates the analysis of results due to lower number of parameters. We verified, via Monte Carlo experiments, whether the studied estimators presented satisfactory results in terms of mean, median, bias, mean square error, mean absolute error and we verified the distribution of the estimates generated by each estimator. Among the main results are: (i) empirical likelihood (EL) estimator - as well as its version with smoothed moment conditions (SEL) - and Bayesian inference (BI) were, in that order, the ones that obtained the best performances, even in misspecification cases; (ii) continuous updating empirical likelihood (CUE), minimum Hellinger distance (HD), exponential tilting (ET) estimators and their smoothed versions exhibit intermediate comparative performance; (iii) performance of exponentially tilted empirical likelihood (ETEL), exponential tilting Hellinger distance (ETHD) and its smoothed versions was seriously compromised by atypical estimates; (iv) smoothed and non-smoothed GEL/GMC estimators exhibit very similar performances; (v) GMM, especially in the over-identified case, and ML estimators had lower performance than their competitors

Cette thèse est consacrée à tester la présence de changements dans les paramètres d'un modèle de régression non-linéaire ainsi que dans un modèle de régression linéaire en très grande dimension. Tout d'abord, nous proposons une méthode basée sur la vraisemblance empirique pour tester la présence de changements dans les paramètres d'un modèle de régression non-linéaire. Sous l'hypothèse nulle, nous prouvons la consistance et la vitesse de convergence des estimateurs des paramètres de régression. La loi asymptotique de la statistique de test sous l'hypothèse nulle nous permet de trouver la valeur critique asymptotique. D'autre part, nous prouvons que la puissance asymptotique de la statistique de test proposée est égale à 1. Le modèle épidémique avec deux points de rupture est également étudié. Ensuite, on s'intéresse à construire les régions de confiance asymptotiques pour la différence entre les paramètres de deux phases d'un modèle non-linéaire avec des regresseurs aléatoires en utilisant la méthode de vraisemblance empirique. On montre que le rapport de la vraisemblance empirique a une distribution asymptotique χ2. La méthode de vraisemblance empirique est également utilisée pour construire les régions de confiance pour la différence entre les paramètres des deux phases d'un modèle non-linéaire avec des variables de réponse manquantes au hasard (Missing At Random (MAR)). Afin de construire les régions de confiance du paramètre en question, on propose trois statistiques de vraisemblance empirique : la vraisemblance empirique basée sur les données cas-complète, la vraisemblance empirique pondérée et la vraisemblance empirique par des valeurs imputées. On prouve que les trois rapports de vraisemblance empirique ont une distribution asymptotique χ2. Un autre but de cette thèse est de tester la présence d'un changement dans les coefficients d'un modèle linéaire en grande dimension, où le nombre des variables du modèle peut augmenter avec la taille de l'échantillon. Ce qui conduit à tester l'hypothèse nulle de non-changement contre l'hypothèse alternative d'un seul changement dans les coefficients de régression. Basée sur les comportements asymptotiques de la statistique de rapport de vraisemblance empirique, on propose une simple statistique de test qui sera utilisée facilement dans la pratique. La normalité asymptotique de la statistique de test proposée sous l'hypothèse nulle est prouvée. Sous l'hypothèse alternative, la statistique de test diverge / In this PHD thesis, we propose a nonparametric method based on the empirical likelihood for detecting the change in the parameters of nonlinear regression models and the change in the coefficient of linear regression models, when the number of model variables may increase as the sample size increases. Firstly, we test the null hypothesis of no-change against the alternative of one change in the regression parameters. Under null hypothesis, the consistency and the convergence rate of the regression parameter estimators are proved. The asymptotic distribution of the test statistic under the null hypothesis is obtained, which allows to find the asymptotic critical value. On the other hand, we prove that the proposed test statistic has the asymptotic power equal to 1. The epidemic model, a particular case of model with two change-points, under the alternative hypothesis, is also studied. Afterwards, we use the empirical likelihood method for constructing the confidence regions for the difference between the parameters of a two-phases nonlinear model with random design. We show that the empirical likelihood ratio has an asymptotic χ2 distribu- tion. Empirical likelihood method is also used to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with response variables missing at randoms (MAR). In order to construct the confidence regions of the parameter in question, we propose three empirical likelihood statistics : empirical likelihood based on complete-case data, weighted empirical likelihood and empirical likelihood with imputed va- lues. We prove that all three empirical likelihood ratios have asymptotically χ2 distributions. An another aim for this thesis is to test the change in the coefficient of linear regres- sion models for high-dimensional model. This amounts to testing the null hypothesis of no change against the alternative of one change in the regression coefficients. Based on the theoretical asymptotic behaviour of the empirical likelihood ratio statistic, we propose, for a deterministic design, a simpler test statistic, easier to use in practice. The asymptotic normality of the proposed test statistic under the null hypothesis is proved, a result which is different from the χ2 law for a model with a fixed variable number. Under alternative hypothesis, the test statistic diverges

Disposant d’un jeu de données sur des infections nosocomiales, nous utilisons des techniques de vraisemblance empirique pour construire des bandes de confiance pour certaines quantité d’intérêt. Cette étude nous amène à renforcer les outils déjà existants afin qu’ils s’adaptent à notre cadre. Nous présentons dans une première partie les outils mathématiques issus de la littérature que nous utilisons dans ce travail de thèse. Nous les appliquons ensuite à diverses situations et donnons de nouvelles démonstrations lorsque cela est nécessaire. Nous conduisons aussi des simulations et obtenons des résultats concrets concernant notre jeu de données. Enfin, nous détaillons les algorithmes utilisés. / The starting point of this thesis is a data set of nosocomial infectionsin an intensive care unit of a French hostipal. We focused our attention onbuilding confidence bands for some parameters of interest using empiricallikelihood techniques. In order to do so, we had to adapt and develop somealready existing methods so that they fit our setup.We begin by giving a state of the art of the different theories we use.We then apply them to different setups and demonstrate new results whenneeded. Finally, we conduct simulations and describe our algorithms.

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In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) approach to construct goodness-of-fit test and provide estimates for the Cox model with various types of censored data. Specifically, the problems under consideration are the two-sample Cox model and stratified Cox model with right censored data, doubly censored data and partly interval-censored data. Related computational issues are discussed, and some simulation results are presented. The procedures developed in the work are applied to several real data sets with some discussion.