Open Access
December 2004 Local linear spatial regression
Marc Hallin, Zudi Lu, Lanh T. Tran
Ann. Statist. 32(6): 2469-2500 (December 2004). DOI: 10.1214/009053604000000850


A local linear kernel estimator of the regression function xg(x):=E[Yi|Xi=x], x∈ℝd, of a stationary (d+1)-dimensional spatial process {(Y i,Xi),i∈ℤN} observed over a rectangular domain of the form ℐn:={i=(i1,…,iN)∈ℤN|1≤iknk,k=1,…,N}, n=(n1,…,nN)∈ℤN, is proposed and investigated. Under mild regularity assumptions, asymptotic normality of the estimators of g(x) and its derivatives is established. Appropriate choices of the bandwidths are proposed. The spatial process is assumed to satisfy some very general mixing conditions, generalizing classical time-series strong mixing concepts. The size of the rectangular domain ℐn is allowed to tend to infinity at different rates depending on the direction in ℤN.


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Marc Hallin. Zudi Lu. Lanh T. Tran. "Local linear spatial regression." Ann. Statist. 32 (6) 2469 - 2500, December 2004.


Published: December 2004
First available in Project Euclid: 7 February 2005

zbMATH: 1069.62075
MathSciNet: MR2153992
Digital Object Identifier: 10.1214/009053604000000850

Primary: 62G05
Secondary: 60J25 , 62J02

Keywords: asymptotic normality , local linear kernel estimate , Mixing random field , spatial regression

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 6 • December 2004
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