http://worldcat.org/entity/work/id/137252984

Bayes Estimation of a Multivariate Density

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).

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