Date of this Version
Electronic Journal of Statistics
A commonly used semiparametric partial linear model is considered. We propose analyzing this model using a difference based approach. The procedure estimates the linear component based on the differences of the observations and then estimates the nonparametric component by either a kernel or a wavelet thresholding method using the residuals of the linear fit. It is shown that both the estimator of the linear component and the estimator of the nonparametric component asymptotically perform as well as if the other component were known. The estimator of the linear component is asymptotically efficient and the estimator of the nonparametric component is asymptotically rate optimal. A test for linear combinations of the regression coefficients of the linear component is also developed. Both the estimation and the testing procedures are easily implementable. Numerical performance of the procedure is studied using both simulated and real data. In particular, we demonstrate our method in an analysis of an attitude data set.
asymptotic efficiency, difference-based method, kernel method, wavelet thresholding method, partial linear model, semiparametric model
Wang, L., Brown, L. D., & Cai, T. (2011). A Difference Based Approach to the Semiparametric Partial Linear Model. Electronic Journal of Statistics, 5 619-641. http://dx.doi.org/10.1214/11-EJS621
Date Posted: 27 November 2017
This document has been peer reviewed.