ABSTRACT

Most realistic estimation problems involve vector parameters. In univariate studies the simplest problems with more than one parameter tend to be those of location and scale, but many others occur where the data distribution F depends on more than one parameter. In the usual general linear model it is reasonable to assume that the covariance matrix of the estimates of the parameters of interest is known apart from a multiplicative constant, the residual variance. This leads to a special class of Empirical Bayes (EB) problems, and in particular, those involving the multivariate normal distribution with known covariance matrix. Moreover calculation of Bayes and EB estimates tends to be difficult in these cases, involving tedious integration. Study of the multivariate normal can be defended on the grounds that essentially multivariate data often are collected and analysed, and the EB sampling scheme may well apply to such collections.