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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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