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- W2074895514 abstract "Let (X, Y) be a Rd×R-valued random vector. In regression analysis one wants to estimate the regression function m(x)≔E(Y|X=x) from a data set. In this paper we consider the rate of convergence for the k-nearest neighbor estimators in case that X is uniformly distributed on [0,1]d, Var(Y|X=x) is bounded, and m is (p, C)-smooth. It is an open problem whether the optimal rate can be achieved by a k-nearest neighbor estimator for 1<p≤1.5. We solve the problem affirmatively. This is the main result of this paper. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected L2 error." @default.
- W2074895514 created "2016-06-24" @default.
- W2074895514 creator A5056491589 @default.
- W2074895514 date "2012-09-01" @default.
- W2074895514 modified "2023-09-26" @default.
- W2074895514 title "Rates of convergence for the k-nearest neighbor estimators with smoother regression functions" @default.
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- W2074895514 doi "https://doi.org/10.1016/j.jspi.2012.03.012" @default.
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