 Nonparametric estimation of multivariate elliptic densities via finite mixture sievesHeather Battey and Oliver Linton Journal of Multivariate Analysis, 2014, vol. 123, issue C, 43-67 Abstract: This paper considers the class of p-dimensional elliptic distributions (p≥1) satisfying the consistency property (Kano, 1994) [23] and within this general framework presents 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) [20] 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 semiparametric estimators. The rate performance of our estimator depends on the tail behaviour of the underlying mixing density (and hence that of the data) rather than smoothness properties. In fact, our method achieves a rate of at least Op(n−1/4), provided only some positive moment exists. When further moments exists, the rate improves reaching Op(n−3/8) as the tails of the true density converge to those of a normal. Unlike the elliptic density estimator of Liebscher (2005) [25], our sieve estimator always yields an estimate that is a valid density, and is also attractive from a practical perspective as it accepts data as a stream, thus significantly reducing computational and storage requirements. Monte Carlo experimentation indicates encouraging finite sample performance over a range of elliptic densities. The estimator is also implemented in a binary classification task using the well-known Wisconsin breast cancer dataset. Date: 2014 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:123:y:2014:i:c:p:43-67 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2013.08.013 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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