ABSTRACT
The empirical likelihood (EL) method is one of a growing array of artificial or approximate likelihood-based methods currently in use in statistical practice (Owen, 1990). Interest and the resulting impact in EL methods continue to grow rapidly. In this chapter, we focus on the performance of EL constructs relative to ordinary parametric likelihood ratio-based procedures in the context of clinical experiments. This chapter first offers an overview of the classical EL methods. It explains the similarity between EL functions and parametric likelihood functions, detailed expressions of the Lagrange multipliers up to the fourth derivatives, and asymptotic properties of the EL likelihood functions. This chapter also deals with the cases with extra estimating equation information, density-based EL methods, building a composite hypotheses test, Bayesian approaches, Bartlett correction, interpretation of the EL as an empirical goodness of fit test, and some comparison with bootstrap methods. Relevant R codes are provided for practitioners.
