chapter  6
38 Pages

Empirical Likelihood

ByAlbert Vexler, Alan D. Hutson, Xiwei Chen

The empirical likelihood (EL) method is one of a growing array of artificial or approximate likelihood-based methods currently in use in statistical practice. Interest and the resulting impact in EL methods continue to grow rapidly. Perhaps more importantly, EL methods now have various vital applications in expanding numbers of areas of clinical studies. This chapter focuses on the performance of EL constructions relative to ordinary parametric likelihood ratio–based procedures in the context of clinical experiments. The statistical literature has shown that tests derived from empirical likelihood methodology possess many of the same asymptotic properties as those based on parametric likelihoods. This leads naturally to the idea of using empirical likelihood instead of parametric likelihood as the basis for Bayesian inference. This Bayesian empirical likelihood method provides a robust nonparametric data-driven alternative to the more classical Bayesian procedures.