Local linear spatial regression
Marc Hallin, Zudi Lu, Lanh T. Tran
The Annals of Statistics · 2004 · Volume 32 · Issue 6
DOI: 10.1214/009053604000000850
Abstract
A local linear kernel estimator of the regression function x↦g(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≤ik≤nk,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.
Keywords
60J25, 62G05, 62J02, asymptotic normality, local linear kernel estimate, Mixing random field, spatial regression
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