A Renewable Estimation Method for Partially Linear Regression Models

In this paper, we implement renewable estimation for partially linear regression models. Under traditional regularity conditions, the consistency and asymptotic normality of the renewable parameter estimation are established, as well as the properties of renewable nonparametric estimations. In addition, we demonstrate the computational efficiency of the renewable estimations, showing that when the sample size per block is smaller than the number of data blocks, our method can significantly reduce the estimation time compared to the estimation using the full dataset. We conduct simulation experiments to demonstrate the superiority and the efficiency of the proposed procedure, and apply the renewable estimation method to analyze the air quality data.