Multivariate Setup Research Articles

Estimation of Generalized Variance Under Entropy Losses : Admissibility Results

We consider the problem of estimating the generalized variance in a multivariate normal setup. The best affine equivariant estimates of | ∑ | are found to be admissible in the class of all estimates depending on the determinant of the Wishart matrix only under entropy losses.

Some new approaches to multivariate probability distributions

We extend and generalize to the multivariate set-up our earlier investigations related to expected remaining life functions and general hazard measures including representations and stability theorems for arbitrary probability distributions in terms of these concepts. (The univariate case is discussed in detail in Kotz and Shanbhag, Advan. Appl. Probab. 12 (1980), 903–921.)

A Note on Multivariate Calibration Experiments

This paper is concerned with multivariate calibration experiments. It provides a Bayesian procedure appropriate when one instrument out of K available has to be chosen as a quick and cheap alternative to long and costly laboratory methods. We use a multivariate extension of a calibration experiment taken from Aitchison and Dunsmore (1975, Chap. 10) to describe the problem. Suppose that a new autoanalyzer is needed in a hospital for the routine determination of the concentration of p enzymes in blood plasma samples. To evaluate the effectiveness of the autoanalyzer, each of n plasma samples is divided into two aliquots, one being assigned to the laboratory method and the other to the analyzer determination. The autoanalyzer is designed to give a 1 x q vector of readings for each plasma sample. For a new plasma sample, it gives a certain vector of q readings. What can be said about the p enzyme concentrations? Much research on statistical calibration has dealt with this estimation problem (e.g., Williams, 1959; Brown, 1982). For univariate calibration experiments, see, for example, Krutchkoff (1967), Williams (1969), Hoadley (1970), and Hunter and Lamboy (1981). We examine instead the problem arising when one out of K different autoanalyzers has to be chosen. We assume that the cost of buying and/or utilizing the kth one is Ck and that the kth autoanalyzer gives a 1 x qk vector of readings, k = 1, ... , K. In order to evaluate the effectiveness of each instrument and to be able to make an optimal choice, a criterion based on Shannon information is used in ?3. In ?2 we consider the multivariate calibration setup as given in Brown (1982) and report the Bayesian results of his ?3. Section 4 deals briefly with the extension to unequal costs and with the problem of testing the redundancy of a subset of responses. An example is included in ?5.