Testing for parametric component of partially linear models with missing covariates

This paper considers the testing problem of partially linear models with missing covariates. The inverse probability weighted restricted estimator for the parametric component under linear constraint is derived and proven to share asymptotically normal distribution. To test the linear constraint, we construct two test statistics based on the the Lagrange multiplier and the empirical likelihood methods. The limiting distributions of the resulting test statistics are both standard chi-squared distributions under the null hypothesis. Simulation studies and a real data analysis are conducted to illustrate relevant performances.