Statistics Papers

Document Type

Journal Article

Date of this Version

2011

Publication Source

Electronic Journal of Statistics

Volume

5

Start Page

619

Last Page

641

DOI

10.1214/11-EJS621

Abstract

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.

Keywords

asymptotic efficiency, difference-based method, kernel method, wavelet thresholding method, partial linear model, semiparametric model

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Date Posted: 27 November 2017

This document has been peer reviewed.