Penalized empirical likelihood for high-dimensional partially linear varying coefficient model with measurement errors

For the high-dimensional partially linear varying coefficient models where covariates in the nonparametric part are measured with additive errors, we, in this paper, study asymptotic distributions of a corrected empirical log-likelihood ratio function and maximum empirical likelihood estimator of the regression parameter. At the same time, based on penalized empirical likelihood (PEL) approach, the parameter estimation and variable selection of the model are investigated, the proposed PEL estimators are shown to possess the oracle property. Also, we introduce the PEL ratio statistic to test a linear hypothesis of the parameter and prove it follows an asymptotically chi-square distribution under the null hypothesis. Simulation study and real data analysis are undertaken to evaluate the finite sample performance of the proposed methods.