The Annals of Statistics

Local linear spatial regression

Marc Hallin, Zudi Lu, and Lanh T. Tran

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 7 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1107794876

Digital Object Identifier
doi:10.1214/009053604000000850

Mathematical Reviews number (MathSciNet)
MR2153992

Zentralblatt MATH identifier
1069.62075

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

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

Citation

Hallin, Marc; Lu, Zudi; Tran, Lanh T. Local linear spatial regression. Ann. Statist. 32 (2004), no. 6, 2469--2500. doi:10.1214/009053604000000850. https://projecteuclid.org/euclid.aos/1107794876


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