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Kernel regression estimation for continuous spatial processes

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Abstract

We investigate here a kernel estimate of the spatial regression function r(x) = E(Y u | X u = x), x ∈ ℝd, of a stationary multidimensional spatial process { Z u = (X u, Y u), u ∈ ℝN}. 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 ℝN. 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.

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Authors and Affiliations

  1. Univ. Charles De Gaulle, Lille, France

    S. Dabo-Niang

  2. Univ. Aix-Marseille 2, France

    A. -F. Yao

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  1. S. Dabo-Niang
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  2. A. -F. Yao
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Correspondence to S. Dabo-Niang.

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Dabo-Niang, S., Yao, A.F. Kernel regression estimation for continuous spatial processes. Math. Meth. Stat. 16, 298–317 (2007). https://doi.org/10.3103/S1066530707040023

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  • DOI: https://doi.org/10.3103/S1066530707040023

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