In this paper, we use the empirical likelihood method to construct theconfidence regions for the difference between the parameters of a two-phasesnonlinear model with random design. We show that the empirical likelihood ratiohas an asymptotic chi-squared distribution. The result is a nonparametricversion of Wilk's theorem. Empirical likelihood method is also used toconstruct the confidence regions for the difference between the parameters of atwo-phases nonlinear model with response variables missing at randoms (MAR). Inorder to construct the confidence regions of the parameter in question, wepropose three empirical likelihood statistics : Empirical likelihood based oncomplete-case data, weighted empiri- cal likelihood and empirical likelihoodwith imputed values. We prove that all three empirical likelihood ratios haveasymptotically chi-squared distributions. The effectiveness of the proposedapproaches in aspects of coverage probability and interval length isdemonstrated by a Monte-Carlo simulations.
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