Econometric Theory

ARTICLES

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

Efang Konga1, Oliver Lintona2 c1 and Yingcun Xiaa3

a1 Technische Universiteit Eindhoven

a2 London School of Economics

a3 Nanjing University, China and National University of Singapore

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.

Correspondence

c1 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.

Footnotes

Xia’s research is partially supported by the National Natural Science Foundation of China (10471061) and a research grant from RMI, National University of Singapore.

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