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Heather Battey, Cambridge U. Print
Monday, 09 May 2011, 14:30 - 15:30

Heather Battey (University of Cambridge)

Nonparametric estimation of multivariate elliptic densities via finite mixture sieves

Abstract: Owing to generality considerations and breadth of application, density estimation is one of the most actively studied challenges in statistics. Although nonparametric density estimation was advanced dramatically by the introduction of the kernel density estimator (Fix and Hodges, 1951; Rosenblatt, 1956), the performance of this estimator deteriorates rapidly for a fixed sample size as the number of dimensions grows large. This provides motivation for restricting the set of all p-dimensional Lebesgue densities (P>=1) to a smaller class (one that embeds many naturally arising examples) and estimating nonparametrically within that class. In this talk I consider the restriction to the class of p-dimensional elliptic densities satisfying the consistency property (Kano, 1994) and, within this framework, present a two-stage nonparametric estimator for the Lebesgue density based on Gaussian mixture sieves. Under the on-line Exponentiated Gradient (EG) algorithm of Helmbold et al. (1997) and without restricting the mixing measure to have compact support, the estimator produces estimates converging uniformly in probability to the true elliptic density at a rate that is independent of the dimension of the problem, hence circumventing the familiar curse of dimensionality inherent to many nonparametric estimators. Finite sample performance and practical implications are also discussed.

Location: R 42.2.113
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