Empirical likelihood and variable selection for partially linear single-index EV models with missing censoring indicators

In this paper, we focus on the empirical likelihood inference for partially linear single-index errors-in-variables (EV) models when the data are right censored and the censoring indicator is missing at random (MAR). Two bias-corrected empirical log-likelihood ratio (BCELR) functions for the parameters by using regressing calibration and imputation methods are introduced. The limiting distributions of the BCELRs are shown to have a mixture of central chi-squared distribution. Based on this, the confidence regions of the parameters can be constructed by using bootstrap approximation. Furthermore, as there would be some spurious covariates in the linear and nonlinear parts, a penalized empirical likelihood (PEL) approach is proposed with the help of smoothly clipped absolute deviation penalty. Two proposed PEL estimators are shown to possess the oracle property. A simulation study and a real data analysis are conducted to evaluate the finite sample performance of the proposed methods.