Kernel regression estimation for continuous spatial processes |
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Authors: | S. Dabo-Niang A. -F. Yao |
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Affiliation: | (1) Univ. Charles De Gaulle, Lille, France;(2) Univ. Aix-Marseille 2, France |
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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 ∈ ℝ 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 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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Keywords: | kernel density estimation kernel regression estimation spatial process spatial prediction optimal rate of convergence |
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