Note on nonparametric $M$-estimation for spatial regression

A. Gheriballaha and R. Rouaneb,*

Note on nonparametric $M$-estimation for spatial regression

Authors :

A. Gheriballah^a and R. Rouane^b,*

Author Address :

^a,bLaboratory of Statistical and stochastic processes, Univ. Djillali Liabs, BP 89, 22000 Sidi Bel Abbs, Algeria.

Abstract :

In this paper, we investigate a nonparametric robust estimation for spatial regression. More precisely, given a strictly stationary random field $Z_{mathbf{i}}=(X_{mathbf{i}},Y_{mathbf{i}})$, $mathbf{i}inmathbb{N}^{ N}$, 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, $p$-mean consistency, Nonparametric regression, Spatial process, Robust estimation.

DOI :

Article Info :

Received : February 28, 2013; Accepted : November 25, 2013.