Statistical inferences for varying coefficient partially non linear model with missing covariates

In this article, we consider the statistical inferences for varying coefficient partially non linear model with missing covariates. The purpose of this article is two-fold. First, we propose an inverse probability weighted profile non linear least squares technique for estimating the unknown parameter and the non parametric function, and the asymptotic normality of the resulting estimators are proved. Second, we consider empirical likelihood inferences for the unknown parameter and non parametric function. The empirical log-likelihood ratio function for the unknown parameter vector in the non linear function part and a residual-adjusted empirical log-likelihood ratio function for the non parametric component are proposed. The corresponding Wilks phenomena are obtained and the confidence regions for the parameter and the point-wise confidence intervals for coefficient function are constructed. Simulation studies and real data analysis are conducted to examine the finite sample performance of the proposed methods.