ABSTRACT
This chapter discusses methods to combine likelihood functions in parametric or empirical form in the setting of two-group comparison. It demonstrates an inference on incomplete bivariate data using a method that combines the parametric model and empirical likelihoods. These types of approaches make it possible to use all information in the form of bivariate data whether completely or incompletely observed. This chapter starts with discussions of two-group comparison of means where the empirical likelihood ratio (ELR) test statistic carries out the mean-specific comparisons unlike other available nonparametric tests. It discusses comparison of multivariate means as a simple extension of univariate two-group comparison. The profile analysis is discussed as a relevant example of the multivariate mean test. Then, the likelihood ratio test based on the combined likelihood for the incomplete and complete data is developed to compare two treatment groups. We show that the power can be augmented by combining relevant information. Relevant R codes are provided for practitioners.
