Nonparametric estimation of a regression function using the gamma kernel method in ergodic processes

2016/05/24 by Agostinho Rosa, Rosa, A. C., Maria-Ines Nogueira +1
Computer Science · Mathematics · #60F05 #60F15 (Secondary) #62G08 #62M10 (Primary) #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1605.07520

openalex publication_date 2016/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the nonparametric estimation of density and regression functions with non-negative support using a gamma kernel procedure introduced by Chen (2000). Strong uniform consistency and asymptotic normality of the corresponding estimators are established under a general ergodic assumption on the data generation process. Our results generalize those of Shi and Song (2016), obtained in the classic i.i.d. framework, and the works of Bouezmarni and Rombouts (2008, 2010b) and Gospodinov and Hirukawa (2007) for mixing time series.

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