The Annals of Statistics

Local linear spatial regression

Marc Hallin, Zudi Lu, and Lanh T. Tran

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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.

Article information

Ann. Statist., Volume 32, Number 6 (2004), 2469-2500.

First available in Project Euclid: 7 February 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 60J25: Continuous-time Markov processes on general state spaces 62J02: General nonlinear regression

Mixing random field local linear kernel estimate spatial regression asymptotic normality


Hallin, Marc; Lu, Zudi; Tran, Lanh T. Local linear spatial regression. Ann. Statist. 32 (2004), no. 6, 2469--2500. doi:10.1214/009053604000000850.

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