Convergence of functional k-nearest neighbor regression estimate with functional responses
نویسندگان
چکیده
منابع مشابه
Rates of convergence of the functional k-nearest neighbor estimate
Let F be a separable Banach space, and let (X, Y ) be a random pair taking values in F×R. Motivated by a broad range of potential applications, we investigate rates of convergence of the k-nearest neighbor estimate rn(x) of the regression function r(x) = E[Y |X = x], based on n independent copies of the pair (X, Y ). Using compact embedding theory, we present explicit and general finite sample ...
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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 ...
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ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2011
ISSN: 1935-7524
DOI: 10.1214/11-ejs595