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Submitted by pscully on Fri, 02/06/2009 - 10:30.
02/12/2009 - 16:10
02/12/2009 - 17:30
STA/BST 290: David Mason
Estimators of Integral Functionals of the Density Function
Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)
M. Mason (Univ.
Title: Estimators of Integral Functionals of the Density Function
Abstract: For several decades there has been considerable interest in the problem of estimating integral functionals of the density function of the form
where f is a Lebesgue density, f(i) denotes its ith derivative and F is its cumulative distribution function. Such integral functionals appear in the asymptotic variance of certain nonparametric statistics. They also arise in a number of bandwidth selection procedures for density estimators. We use recent results on local U–statistics to prove consistency and asymptotic normality (uniform in bandwidth) of the Levit (1978) type estimator of T (F) given by
for appropriate U–statistic-type estimators
We shall also motivate a reasonable procedure for choosing bandwidths based on the data. This talk is based on a joint paper with Evarist Giné, which recently appeared in the Scandinavian Journal of Statistics.