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Uniform Bahadur Representation for Local Polynomial Estimates of M-Regression and Its Application to The Additive Model

Kong, Efang, Linton, Oliver, Xia, Yingcun (2010) Uniform Bahadur Representation for Local Polynomial Estimates of M-Regression and Its Application to The Additive Model. Uniform Bahadur Representation for Local Polynomial Estimates of M-Regression and Its Application to The Additive Model, 26 (5). pp. 1529-1564. ISSN 0266-4666. (doi:10.1017/S0266466609990661)

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 in such estimators into other functionals where some control over higher order terms are required. We apply our results to the estimation of an additive M-regression model.

Item Type: Article
DOI/Identification number: 10.1017/S0266466609990661
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Efang Kong
Date Deposited: 29 Mar 2010 11:46 UTC
Last Modified: 28 May 2019 15:18 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/23952 (The current URI for this page, for reference purposes)
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