On the convergence rate of maximal deviation distribution for kernel regression estimates
Let (X, Y), X [set membership, variant] Rp, Y [set membership, variant] R1 have the regression function r(x) = E(Y|X = x). We consider the kernel nonparametric estimate rn(x) of r(x) and obtain a sequence of distribution functions approximating the distribution of the maximal deviation with power rate. It is shown that the distribution of the maximal deviation tends to double exponent (which is a conventional form of such theorems) with logarithmic rate and this rate cannot be improved.
Volume (Year): 15 (1984)
Issue (Month): 3 (December)
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