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UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL

Published online by Cambridge University Press:  05 March 2010

Efang Kong
Affiliation:
Technische Universiteit Eindhoven
Oliver Linton*
Affiliation:
London School of Economics
Yingcun Xia
Affiliation:
Nanjing University, China and National University of Singapore
*
*Address for correspondence to Oliver Linton, Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom; e-mail: o.linton@lse.ac.uk.

Abstract

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Yi, Xi)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We apply our results to the estimation of an additive M-regression model.

Type
ARTICLES
Copyright
Copyright © Cambridge University Press 2010

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