Empirical likelihood confidence regions for the parameters of a two phases nonlinear model with and without missing response data

Abstract

ABSTRACTIn this article, we use the empirical likelihood method to construct the confidence regions for the difference between the parameters of a two-phase nonlinear model with random design. We show that the empirical likelihood ratio has an asymptotic chi-squared distribution. The result is a nonparametric version of Wilks’ theorem. The empirical likelihood method is also used to construct the confidence regions for the difference between the parameters of a two-phase nonlinear model with response variables missing at randoms (MAR). In order to construct the confidence regions of the parameter in question, we propose three empirical likelihood statistics: empirical likelihood based on complete-case data, weighted empirical likelihood, and empirical likelihood with imputed values. We prove that all three empirical likelihood ratios have asymptotically chi-squared distributions. The effectiveness of the proposed approaches in aspects of coverage probability and interval length is demonstrated by Monte Ca...