Variance estimation for semiparametric regression models by local averaging

Variance estimation is a fundamental problem in statistical modelling and plays an important role in the inferences after model selection and estimation. In this paper, we focus on several nonparametric and semiparametric models and propose a local averaging method for variance estimation based on the concept of partial consistency. The proposed method has the advantages of avoiding the estimation of the nonparametric function and reducing the computational cost and can be easily extended to more complex settings. Asymptotic normality is established for the proposed local averaging estimators. Numerical simulations and a real data analysis are presented to illustrate the finite sample performance of the proposed method.