Empirical Likelihood Inference Under Density Ratio Models Based on Type I Censored Samples: Hypothesis Testing and Quantile Estimation

Abstract

We present a general empirical likelihood inference framework for Type I censored multiple samples. Based on this framework, we develop an effective empirical likelihood ratio test and efficient distribution function and quantile estimation methods for Type I censored samples. In particular, we pool information across multiple samples through a semiparametric density ratio model and propose an empirical likelihood approach to data analysis. This approach achieves high efficiency without making risky model assumptions. The maximum empirical likelihood estimator is found to be asymptotically normal. The corresponding empirical likelihood ratio is shown to have a simple chi-square limiting distribution under the null model of a composite hypothesis about the DRM parameters. The power of the EL ratio test is also derived under a class of local alternative models. Distribution function and quantile estimators based on this framework are developed and are shown to be more efficient than the empirical estimators based on single samples. Our approach also permits consistent estimations of distribution functions and quantiles over a broader range than would otherwise be possible. Simulation studies suggest that the proposed distribution function and quantile estimators are more efficient than the classical empirical estimators, and are robust to outliers and misspecification of density ratio functions. Simulations also show that the proposed EL ratio test has superior power compared to some semiparametric competitors under a wide range of population distribution settings.