Introduction and Brief Survey
Multivariate analysis originated with problems of statistical inference in the work of Pearson and Fisher, men with thorough grounding in applied statistics. The first important book on the subject, Anderson (1958) gives a balanced view of the subject by treating, in each case, first the question of inference, and then, the calculation of the multivariate density function of the resulting multivariate statistic, most often for a likelihood ratio test. At that time the multivariate statistics considered had density functions. In the past decade study of estimators of multivariate parameters of Poisson and negative binomial random variables has made discrete problems an important part of multivariate inference. Material about discrete problems was outside the scope of Anderson (1958) and remains outside the scope of recent books such as Eaton (1983) and Muirhead (1982).
KeywordsManifold Covariance Convolution Hunt Stein
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