Empirical likelihood for single index model with missing covariates at random

Author： Guo Xu Niu Cuizhen Yang Yiping Xu Wangli

E-ISSN： 1029-4910|49|3|588-601

ISSN： 0233-1888

Source： Statistics, Vol.49, Iss.3, 2015-05, pp. : 588-601

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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.