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

2007/09/11 by Efang Kong, Oliver Linton, Kong, Efang +3
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.0709.1663

40 pages

openalex publication_date 2007/09/11 · arxiv created 2007/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes \(Y_i,\underlineX_i)\. 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.

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