Kernel regression estimation for continuous spatial processes

We investigate here a kernel estimate of the spatial regression function r(x) = E(Y ^sub u^ | X ^sub u^ = x), x ^sup d^ , of a stationary multidimensional spatial process { Z ^sub u^ = (X ^sub u^ , Y ^sub u^ ), u ^sup N^ }. The weak and strong consistency of the estimate is shown under sufficient co...

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Bibliographic Details
Published in:Mathematical methods of statistics 2007-12, Vol.16 (4), p.298-317
Main Authors: Dabo-Niang, S., Yao, A. -F.
Format: Article
Language:English
Subjects:
Mathematics
Statistics
Statistics Theory
Studies
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Summary:We investigate here a kernel estimate of the spatial regression function r(x) = E(Y ^sub u^ | X ^sub u^ = x), x ^sup d^ , of a stationary multidimensional spatial process { Z ^sub u^ = (X ^sub u^ , Y ^sub u^ ), u ^sup N^ }. The weak and strong consistency of the estimate is shown under sufficient conditions on the mixing coefficients and the bandwidth, when the process is observed over a rectangular domain of ^sup N^ . Special attention is paid to achieve optimal and suroptimal strong rates of convergence. It is also shown that this suroptimal rate is preserved by using a suitable spatial sampling scheme.[PUBLICATION ABSTRACT]
ISSN:1066-5307
1934-8045
DOI:10.3103/S1066530707040023