Accession Number : ADA114579

Title :   Bayes Estimation of a Multivariate Density.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Leonard,Tom

PDF Url : ADA114579

Report Date : Feb 1982

Pagination or Media Count : 17

Abstract : The problem addressed concerns the estimation of a p-dimensional multivariate density, given only a set of n observation vectors, together with information that the density function is likely to be reasonably smooth. A solution is proposed which employs up to n + 1/2 p(p+1) smoothing parameters, all of which may be estimated by their posterior means. This avoids the well-known difficulties, associated with even one-dimensional kernel estimators, of estimating the bandwidth or smoothing parameter by a mathematical procedure. The posterior mean value function, unconditional upon the smoothing parameters, turns out to be a data-based mixture of multivariate t-distributions. The corresponding estimate of the sampling covariance matrix may be viewed as a shrinkage estimator of the Bayes-Stein type. The results involve some finite series which may be evaluated by straightforward simulation procedure. (Author)

Descriptors :   *Estimates, *Bayes theorem, *Functions, *Density, Mean, Value, Analysis of variance, Data bases, Mathematical analysis, Multivariate analysis, Shrinkage, Mixtures

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE