# An Introduction to Multivariate Statistical Analysis (Wiley by Theodore W. Anderson

By Theodore W. Anderson

Perfected over 3 versions and greater than 40 years, this box- and classroom-tested reference:* makes use of the strategy of utmost chance to a wide quantity to make sure moderate, and from time to time optimum procedures.* Treats all of the easy and demanding subject matters in multivariate statistics.* provides new chapters, in addition to a couple of new sections.* presents the main methodical, updated info on MV facts to be had.

**Read Online or Download An Introduction to Multivariate Statistical Analysis (Wiley Series in Probability and Statistics) PDF**

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

**Example text**

The matrix ~ ficients of X(ll on X(2). = l: 12l:Z21 is the matrix of regression coef- The element in the ith row and (k - q )th column of ~ = l: 12 l:Z21 is often denoted by (7) i=l, .. q+ I ..... k+ I ..... p' k=q+l, ... ,p. LII) + ~(x(2) - 1-1-(2») is called the regression function. Let u i ",+1. ,' be the i,jth element of l:11'2' We call these partial cuuarial/ces; if,i'" + I. "" is a partial variance. 2 (8) Pij·q + I .... p yu U i j-q+I, .... Iu.. P i,j=l, ... ,q, ' is the partial correlation between Xi and Xj holding Xq + 1, ...

Thus (31) Pr{xl::;X::;xziY=y}= f X2 f(uly)du, XI where f(uiy) = feu, y) /g(y). For given y, feu iy) is a density funct;on and is called the conditional density of X given y. We note that if X and Yare independent, f(xiy) = f(x). In the general case of XI> ... ' XI' with cdf F(x l , ... , xp), the conditional density of Xl' . , X" given X'+I =X,+l' ... ' Xp =x p' is . :-' (32) f oo ···foo f(ul, ... ,u"x,+I, ... ul ... du, _00 _00 For a more general discussion of conditional prObabilities, the reader is referred to Chung (1974), Kolmogorov (1950), Loeve (1977),(1978), and Neveu (1965).

Yp) falls in a region S is If S is the transform of R, that is, if each point of R transforms by (33) into a point of S and if each point of S transforms into R by (34), then (11) is equal to (3U) by the usual theory of transformation of multiple integrals. From this follows the assertion that (36) is the density of Yl , ••• , Yp. 3. 6), where a is positive ang k is chosen so that the integral of (1) over the entire x-axis is unity. The density function of a multivariate normal distribution of XI" ..