Empirical likelihood ratio tests with power one

Abstract

In the 1970s, Professor Robbins and his coauthors extended the Vile and Wald inequality in order to derive the fundamental theoretical results regarding likelihood ratio based sequential tests with power one. The law of the iterated logarithm confirms an optimal property of the power one tests. In parallel with Robbins’s decision-making procedures, we propose and examine sequential empirical likelihood ratio (ELR) tests with power one. In this setting, we develop the nonparametric one- and two-sided ELR tests. It turns out that the proposed sequential ELR tests significantly outperform the classical nonparametric t-statistic-based counterparts in many scenarios based on different underlying data distributions.