
Accession Number : ADA114579
Title : Bayes Estimation of a Multivariate Density.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIVMADISON 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 pdimensional 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 wellknown difficulties, associated with even onedimensional 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 databased mixture of multivariate tdistributions. The corresponding estimate of the sampling covariance matrix may be viewed as a shrinkage estimator of the BayesStein 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