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Empirical Likelihood Method (empirical + likelihood_method)

Distribution by Scientific Domains
Mathematics and Statistics80%

Selected Abstracts

Empirical-likelihood-based difference-in-differences estimators

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2008
Jing Qin
Summary., Recently there has been a surge in econometric and epidemiologic works focusing on estimating average treatment effects under various sets of assumptions. Estimation of average treatment effects in observational studies often requires adjustment for differences in pretreatment variables. Rosenbaum and Rubin have proposed the propensity score method for estimating the average treatment effect by adjusting pretreatment variables. In this paper, the empirical likelihood method is used to estimate average treatment effects on the treated under the difference-in-differences framework. The advantage of this approach is that the common marginal covariate information can be incorporated naturally to enhance the estimation of average treatment effects. Compared with other approaches in the literature, the method proposed can provide more efficient estimation. A simulation study and a real economic data analysis are presented. [source]

Empirical likelihood confidence regions for comparison distributions and roc curves

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2003
Gerda Claeskens
Abstract Abstract: The authors derive empirical likelihood confidence regions for the comparison distribution of two populations whose distributions are to be tested for equality using random samples. Another application they consider is to ROC curves, which are used to compare measurements of a diagnostic test from two populations. The authors investigate the smoothed empirical likelihood method for estimation in this context, and empirical likelihood based confidence intervals are obtained by means of the Wilks theorem. A bootstrap approach allows for the construction of confidence bands. The method is illustrated with data analysis and a simulation study. Résumé: Les auteurs déduisent de la vraisemblance empirique des régions de confiance pour la distribution comparée de deux populations dont on veut tester l'égalité en loi au moyen d'échantillons aléatoires. Une autre application qu'ils considèrent concerne les courbes ROC, qui permettent de comparer les résultats d'un test diagnostique effectué auprès de deux populations. L'estimation proposée par les auteurs dans ce contexte s'appuie sur une méthode de lissage de la vraisemblance empirique qui conduit, gr,ce au théorème de Wilks, aux intervalles de confiance recherchés. Une approche bootstrap permet en outre de construire des bandes de confiance. La méthode est illustrée au moyen de simulations et d'un jeu de données. [source]

Empirical likelihood for linear regression models under imputation for missing responses

THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2001
Qihua Wang
Abstract The authors study the empirical likelihood method for linear regression models. They show that when missing responses are imputed using least squares predictors, the empirical log-likelihood ratio is asymptotically a weighted sum of chi-square variables with unknown weights. They obtain an adjusted empirical log-likelihood ratio which is asymptotically standard chi-square and hence can be used to construct confidence regions. They also obtain a bootstrap empirical log-likelihood ratio and use its distribution to approximate that of the empirical log-likelihood ratio. A simulation study indicates that the proposed methods are comparable in terms of coverage probabilities and average lengths of confidence intervals, and perform better than a normal approximation based method. [source]

Blockwise generalized empirical likelihood inference for non-linear dynamic moment conditions models

THE ECONOMETRICS JOURNAL, Issue 2 2009
Francesco Bravo
Summary, This paper shows how the blockwise generalized empirical likelihood method can be used to obtain valid asymptotic inference in non-linear dynamic moment conditions models for possibly non-stationary weakly dependent stochastic processes. The results of this paper can be used to construct test statistics for overidentifying moment restrictions, for additional moments, and for parametric restrictions expressed in mixed implicit and constraint form. Monte Carlo simulations seem to suggest that some of the proposed test statistics have competitive finite sample properties. [source]

Interpreting Statistical Evidence with Empirical Likelihood Functions

BIOMETRICAL JOURNAL, Issue 4 2009
Zhiwei Zhang
Abstract There has been growing interest in the likelihood paradigm of statistics, where statistical evidence is represented by the likelihood function and its strength is measured by likelihood ratios. The available literature in this area has so far focused on parametric likelihood functions, though in some cases a parametric likelihood can be robustified. This focused discussion on parametric models, while insightful and productive, may have left the impression that the likelihood paradigm is best suited to parametric situations. This article discusses the use of empirical likelihood functions, a well-developed methodology in the frequentist paradigm, to interpret statistical evidence in nonparametric and semiparametric situations. A comparative review of literature shows that, while an empirical likelihood is not a true probability density, it has the essential properties, namely consistency and local asymptotic normality that unify and justify the various parametric likelihood methods for evidential analysis. Real examples are presented to illustrate and compare the empirical likelihood method and the parametric likelihood methods. These methods are also compared in terms of asymptotic efficiency by combining relevant results from different areas. It is seen that a parametric likelihood based on a correctly specified model is generally more efficient than an empirical likelihood for the same parameter. However, when the working model fails, a parametric likelihood either breaks down or, if a robust version exists, becomes less efficient than the corresponding empirical likelihood. [source]