Empirical Likelihood Incorporating the Existence Probability (New Developments in Statistical Model)

Abstract

Empirical likelihood is an effective nonparametric method for statistical inference, having several good properties from both theoretical and practical aspects. One serious problem of empirical likelihood is that its confidence regions can have poor accuracy, especially when the sample size is small, the parameter is multidimensional, and/or the underlying distribution is skewed. Importantly, the fact that the "probability that the empirical likelihood ratio function exists" (hereinafter, referred to as "existence probability") is always lower than 1 is a strong contributor to such poor accuracy. In this paper, we develop a new approach to improvements in coverage accuracy of empirical likelihood inference by incorporating the existence probability into the inference. It is demonstrated in simulation studies how accurate our methods are; they may work well even in small sample, multidimensional, highly skewed situations.