On the convergence rate of maximal deviation distribution for kernel regression estimates

Valentin Konakov and Vladimir Piterbarg ()

Journal of Multivariate Analysis, 1984, vol. 15, issue 3, 279-294

Abstract: 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.

Keywords: Nonparametric; regression; maximal; deviation; distribution; Gaussian; homogeneous; field (search for similar items in EconPapers)
Date: 1984
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Citations: View citations in EconPapers (18)

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