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Empirical likelihood for single index model with missing covariates at random
Authors:Xu Guo  Yiping Yang  Wangli Xu
Institution:1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, People's Republic of China;3. School of Statistics, Renmin University of China, Beijing, People's Republic of China
Abstract:In this paper, we investigate the empirical-likelihood-based inference for the construction of confidence intervals and regions of the parameters of interest in single index models with missing covariates at random. An augmented inverse probability weighted-type empirical likelihood ratio for the parameters of interest is defined such that this ratio is asymptotically standard chi-squared. Our approach is to directly calibrate the empirical log-likelihood ratio, and does not need multiplication by an adjustment factor for the original ratio. Our bias-corrected empirical likelihood is self-scale invariant and no plug-in estimator for the limiting variance is needed. Some simulation studies are carried out to assess the performance of our proposed method.
Keywords:covariates missing at random  inverse selection probability  empirical likelihood  single-index model
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