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

Zahraa Salloum

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arXiv · 1406.3960

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

Zahraa Salloum

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Abstract

In this paper, we use the empirical likelihood method to construct the confidence regions for the difference between the parameters of a two-phases 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 Wilk's theorem. Empirical likelihood method is also used to construct the confidence regions for the difference between the parameters of a two-phases 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 empiri- cal 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 a Monte-Carlo simulations.

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Zahraa Salloum. 2014-06-16. Empirical likelihood confidence regions for the parameters of a two phases nonlinear model with and without missing response data. https://arxiv.org/abs/1406.3960

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