Strong consistency of nearest neighbor regression function estimators
نویسندگان
چکیده
منابع مشابه
Consistency of a Recursive Nearest Neighbor Regression Function Estimate
Let (X, Y) be an IR” x H-valued random vector and let (Xi, Y,),..., (X,, YN) be. a random sample drawn from its distribution. Divide the data sequence into disjoint blocks of length I , ,..., I,, find the nearest neighbor to X in each block and call the corresponding couple (fl, u). It is shown that the estimate m.(X) = Cy=, wfli q/C;=, w,, of m(X) = E( YjX) satisfies E(lm.(X) m(X)(Pj 3 0 (p 2 ...
متن کاملON THE STRONG UNIVERSAL CONSISTENCY OF NEAREST NEIGHBOR REGRESSION FUNCTION ESTIMATESI BY LUC DEVROYE, LAszLO GYORFI, ADAM KRZYZAK AND GABOR
m(x) = Wni(x ; X1 , . . . , Xn)Yi, i 1 and Wni(x; X1 , . . . ,Xn) is 1/k ifXi is one of the k nearest neighbors of x among X1, . . . , Xn , and Wn i is zero otherwise . Note in particular that I' 1 W,1 = 1. The k-nearest neighbor estimate was studied by Cover (1968) . For a survey of other estimates, see, for example, Collomb (1981, 1985) or Gyorfi (1981) . We are concerned with the L1 converge...
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A class of nonparametric regression function estimates generalizing the nearest neighbor estimate of Cover [ 121 is presented. Under various noise conditions, it is shown that the estimates are strongly uniformly consistent. The uniform convergence of the estimates can be exploited to design a simple random search algorithm for the global minimization of the regression function.
متن کاملConsistency of Nearest Neighbor Methods
In this lecture we return to the study of consistency properties of learning algorithms, where we will be interested in the question of whether the generalization error of the function learned by an algorithm approaches the Bayes error in the limit of infinite data. In particular, we will consider consistency properties of the simple k-nearest neighbor (k-NN) classification algorithm (in the ne...
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For estimating the entropy of an absolutely continuous multivariate distribution, we propose nonparametric estimators based on the Euclidean distances between the n sample points and their kn-nearest neighbors, where {kn : n = 1, 2, . . .} is a sequence of positive integers varying with n. The proposed estimators are shown to be asymptotically unbiased and consistent.
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1984
ISSN: 0047-259X
DOI: 10.1016/0047-259x(84)90067-8