The strong uniform convergence of multivariate variable kernel estimates | Zendy

And Luc Devroye | Zendy; Penrod Clark S. | Zendy

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The strong uniform convergence of multivariate variable kernel estimates

Author(s) -

And Luc Devroye,

Penrod Clark S.

Publication year - 1986

Publication title -

canadian journal of statistics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.804

H-Index - 51

eISSN - 1708-945X

pISSN - 0319-5724

DOI - 10.2307/3314798

Subject(s) - mathematics , kernel (algebra) , sequence (biology) , multivariate statistics , kernel density estimation , combinatorics , variable (mathematics) , random variable , convergence (economics) , statistics , mathematical analysis , estimator , economics , economic growth , genetics , biology

We show that sup, completely as, where f is a uniformly continuous density on are independent random vectors with common density f , and f n is the variable kernel estimate Here H ni is the distance between X i and its k th nearest neighbour, K is a given density satisfying some regularity conditions, and k is a sequence of integers with the property that log asn

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