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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
Abstract 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