By Theodore W. Anderson

ISBN-10: 0471360910

ISBN-13: 9780471360919

Perfected over 3 variants and greater than 40 years, this box- and classroom-tested reference:* makes use of the tactic of extreme chance to a wide volume to make sure moderate, and sometimes optimum procedures.* Treats all of the uncomplicated and demanding subject matters in multivariate statistics.* provides new chapters, in addition to a few new sections.* presents the main methodical, up to date info on MV information on hand.

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**Additional info for An Introduction to Multivariate Statistical Analysis (Wiley Series in Probability and Statistics)**

**Sample text**

Cr.. ll·q+I ..... 2 "q+I" .. ,p ) a:II' .. This shows incidentally that any partial variance of a component of X cannot be greater than the variance. 5 CONDmONAL DISTRIBUTIONS; MULTIPLE CORRELATION 39 reduction in variance on going to the conditional distribution. This fact is another reason for considering tiIe multiple correlation coefficient a measure of association between Xi and X(2). That ~(i)X(2) is the best linear predictor of Xi and has the maximum correlation between Xi and linear functions of X(2) depends only on the covariance structure, without regard to normality.

Pearson has also shown that 00 (57) F(xl,x Z) = E piTi(YI)Tj(YZ)' j=O where the so-called tetrachoric functions T/Y) are tabulated in Pearson (1930) up to TI9(Y). Harris and Soms (1980) have studied generalizations of (57). 4. THE DISTRIBUTION OF LINEAR COMBINATIONS OF NORMALLY DISTRIBUTED VARIATES; INDEPENDENCE OF VARIATES; MARGINAL DISTRIBUTIONS One of the reasons that the study of normal multivariate distributions is so useful is that marginal distributions and conditional distributions derived from multivariate normal distributions are also normal distributions.

P. We assume that the transformation from the x-space to the y-space is one-to-one;t the inverse transformation is (34) i = 1, ... ,p. 'More precisely. (XI' ... 'X p ) is positive. , ... , y" be defined by (35) i = 1, . ,p. Y; = Yi( XI'···' Xp), Then the density of YI , ... , ... , Yp) is the Jacobian (37) J(Yl' ... 'Yp) = aX I aYI ax! ayz aX I ayp ax z ax z ayz axz ayp axp ay! axp ayz axp ayp ~ mod We assume the cJerivatives exist, and "mod" means modulus or absolute value of the expression following it.

### An Introduction to Multivariate Statistical Analysis (Wiley Series in Probability and Statistics) by Theodore W. Anderson

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