STATISTICS COLLOQUIUM

THURSDAY, February 12^th, 2009 at 4.10pm, MSB 1147 (Colloquium Room)

Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)

Speaker: David M. Mason (Univ. Delaware)

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 i^th 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.