A Renewable Estimation Method for Partial Linear Regression Models

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