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Asymptotic distribution for a discrete version of integrated square error of multivariate density kernel estimators

By 3000 Coimbra (Portugal)) Univ. de Coimbra Carlos (Dep. de Matematica Tenreiro

Abstract

In this paper we consider the average square error A_n (#pi#)= 1/_n ?"n?_j=_1#left brace#fn(#chi#_j)-f(#chi#_j(#chi#_j)#right brace#"2#pi#(#chi#_ j) where f is the common density of the independent and identically distributed random vectors X_1,..., X_n,f_n is the kernel estimator based on these vectors, and #pi# is a weight function. Using U-statistics technics, a central limit theorem and an asymptotic in probability for A_n (#pi#) are established. Such results enables us to compare the stochastic measures A_n (#pi#) and I_n(#pi#.f) where I_n(#pi#.f)f f_n(x)-f(x) "2(#pi#.f)(x)dx. Applications to goodness-of-fit tests are also consideredAvailable from Departamento de Matematica, Universidade de Coimbra, 3000 Coimbra, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga

Topics: 12A - Pure mathematics
Publisher: Coimbra : Univ. de Coimbra
Year: 1995
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Provided by: OpenGrey Repository
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