ABSTRACT
Over the long course of statistical methodological developments there been a shift from classic parametric likelihood methods to a focus towards robust and efficient nonparametric and semiparametric developments of various “artificial” or “approximate” likelihood techniques. These methods have a wide variety of applications related to biostatistical experiments. Many nonparametric and semiparametric approximations to powerful parametric likelihood procedures have been used routinely in both statistical theory and practice. Various studies have shown that artificial or approximate likelihood-based techniques efficiently incorporate information expressed through the data, and have many of the same asymptotic properties as those derived from the corresponding parametric likelihoods. 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 an expanding number of health related studies.
Chapter 10 outlines basic components related to EL techniques and their theoretical evaluations. This chapter demonstrates valuable examples of EL applications. We provide arguments that can be accepted in favor of EL methods in order to be applied in statistical practice. Corresponding R codes are presented.
