Note on nonparametric \(M\)-estimation for spatial regression

A. Gheriballah; R. Rouane

doi:10.26637/mjm201/005

Abstract

In this paper, we investigate a nonparametric robust estimation for spatial regression. More precisely, given a strictly stationary random field \(Z_{\mathbf{i}}=\left(X_{\mathbf{i}}, Y_{\mathbf{i}}\right), \mathbf{i} \in \mathbb{N}^N\), we consider a family of robust nonparametric estimators for a regression function based on the kernel method. We establish a \(p\)-mean consistency results of the kernel estimator under some conditions.

Keywords:

Quadratic error, Nonparametric regression, Spatial process, Robust estimation, \(p\)-mean consistency

Mathematics Subject Classification:

26A33, 34A08, 35R12, 47H10

Authors Imprint References Funding Related Articles Downloads

A. Gheriballah Laboratory of Statistical and stochastic processes, Univ. Djillali Liabs, BP 89, 22000 Sidi Bel Abbs, Algeria.
R. Rouane Laboratory of Statistical and stochastic processes, Univ. Djillali Liabs, BP 89, 22000 Sidi Bel Abbs, Algeria. https://orcid.org/0000-0002-5061-9878

Pages: 35-42
Date Published: 01-01-2014
Vol. 2 No. 01 (2014): Malaya Journal of Matematik (MJM)

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