Open Access
2021 On a class of recursive estimators for spatially dependent observations
Mohamed El Machkouri, Lucas Reding
Author Affiliations +
Electron. J. Statist. 15(2): 4580-4624 (2021). DOI: 10.1214/21-EJS1878


We investigate the mean squared error and the asymptotic normality for a class of recursive kernel estimators based on a sample of spatially dependent observations. Our main result provides sufficient conditions for a spatial version of a recursive estimator introduced by Hall and Patil (1994) to satisfy a central limit theorem. The results are stated for strongly mixing random fields in the sense of Rosenblatt (1956) and for weakly dependent random fields in the sense of Wu (2005).


The authors are grateful to the referees and the associate editor for many helpful comments.


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Mohamed El Machkouri. Lucas Reding. "On a class of recursive estimators for spatially dependent observations." Electron. J. Statist. 15 (2) 4580 - 4624, 2021.


Received: 1 October 2020; Published: 2021
First available in Project Euclid: 23 September 2021

Digital Object Identifier: 10.1214/21-EJS1878

Primary: 60G60 , 62G05 , 62G07 , 62G08 , 62G20

Keywords: asymptotic normality , Density estimation , Lindeberg’s method , m-dependence , physical dependence measure , quadratic mean error , Random fields , Recursive estimator , Regression estimation , Strong mixing , Weak dependence

Vol.15 • No. 2 • 2021
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