Peng Tang

Introduction to Empirical Likelihood

Empirical likelihood is a nonparametric method of inference based on a data-driven likelihood ratio function. It allows the data analyst to use likelihood methods, without having to assume that the data come a known family of distributions. It can be thought of as a bootstrap that does not resample, and as a likelihood without parametric assumption. I will give the background, motivation and definition of empirical likelihood. It can be shown that the empirical likelihood function is the maximum nonparametric likelihood function. We can ignore ties when we apply empirical likelihood to samples with ties. The empirical likelihood ratio function asymptotically follows Wilk’s theorem (1938) for parametric likelihood ratios. I will illustrate the concepts with brief proof and simulation results about the empirical likelihood confidence interval for mean.