Consistency of a recursive nearest neighbor regression function estimate

Luc Devroye and Gary L. Wise

Journal of Multivariate Analysis, 1980, vol. 10, issue 4, 539-550

Abstract: Let (X, Y) be an d - -valued random vector and let (X1, Y1),...,(XN, YN) be a random sample drawn from its distribution. Divide the data sequence into disjoint blocks of length l1, ..., ln, find the nearest neighbor to X in each block and call the corresponding couple (Xi*, Yi*). It is shown that the estimate mn(X) = [Sigma]i = 1n wniYi*/[Sigma]i = 1n wni of m(X) = E{YX} satisfies E{mn(X) - m(X)p} 0 (p >= 1) whenever E{Yp}

Keywords: Consistency; recursive; estimation; regression; function; nearest; neighbors; weak; convergence; nonparametric; estimation (search for similar items in EconPapers)
Date: 1980
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