Nonparametric regression estimation for random fields in a fixed-design

2005/02/04 by Mohamed El Machkouri, Machkouri, Mohamed El
Decision Sciences · Mathematics · #60G60 #62G08 #FOS: Mathematics #Optimal Experimental Design Methods #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST) #math.PR #math.ST #msc:60G60 #msc:62G08 #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0502091

Accepté pour publication dans la revue "Statistical Inference for Stochastic Processes"

arxiv created 2005/02/04 · openalex publication_date 2005/02/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These estimators can attain the optimal rates of uniform convergence and the results apply to a large class of random fields which contains martingale-difference random fields and mixing random fields.

Related

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• Nonparametric regression for locally stationary random fields under stochastic sampling design
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