ABSTRACT
This chapter offers the overview of statistical hypothesis tests and rational of using the empirical likelihood (EL) approach. It discusses that parametric approaches are often based on untestable assumptions. Although practitioners can incorporate tests for the assumptions, such schemes give rise to complicated topics dealing with multiple testing. This chapter also addresses the benefit of using the likelihood approach in details including the principal idea of the Neyman–Pearson Lemma, likelihood ratio tests, and maximum likelihood. Then the EL is introduced as a data-driven likelihood function that is nonparametric and comparatively powerful. This chapter further discusses the EL’s benefits such as constructing efficient statistical tests using Bayesian methods similar to the parametric likelihood and setting up the EL statistics as composite semi- or nonparametric likelihoods.
