Local linear spatial regression

Details Local linear spatial regression Local linear spatial regression

2005-08-30

arxiv.org/abs/math/0508597v1

Annals of Statistics 2004, Vol. 32, No. 6, 2469-2500

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000850 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000850

A local linear kernel estimator of the regression function x\mapsto g(x):=E[Y_i|X_i=x], x\in R^d, of a stationary (d+1)-dimensional spatial process {(Y_i,X_i),i\in Z^N} observed over a rectangular domain of the form I_n:={i=(i_1,...,i_N)\in Z^N| 1\leq i_k\leq n_k,k=1,...,N}, n=(n_1,...,n_N)\in Z^N, 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 I_n is allowed to tend to infinity at different rates depending on the direction in Z^N.

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