Statistics Papers

Document Type

Technical Report

Date of this Version

11-2016

Publication Source

Journal of Statistical Planning and Inference

Volume

178

Start Page

9

Last Page

111

DOI

10.1016/j.jspi.2016.06.005

Abstract

A multivariate semiparametric partial linear model for both fixed and random design cases is considered. In either case, the model is analyzed using a difference sequence approach. The linear component is estimated based on the differences of observations and the functional component is estimated using a multivariate Nadaraya–Watson kernel smoother of the residuals of the linear fit. We show that both components can be asymptotically estimated as well as if the other component were known. The estimator of the linear component is shown to be asymptotically normal and efficient in the fixed design case if the length of the difference sequence used goes to infinity at a certain rate. The functional component estimator is shown to be rate optimal if the Lipschitz smoothness index exceeds half the dimensionality of the functional component argument. We also develop a test for linear combinations of regression coefficients whose asymptotic power does not depend on the functional component. All of the proposed procedures are easy to implement. Finally, numerical performance of all the procedures is studied using simulated data.

Copyright/Permission Statement

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

multivariate semiparametric model, difference-based method, asymptotic efficiency, partial linear model, random field

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Date Posted: 25 October 2018

This document has been peer reviewed.