An Introduction to Multivariate Statistical AnalysisThe multivariate normal distribution; Estimation of the mean vector and the covariance matrix; The distributions and uses of sample correlation coefficients; The generalized T2 statistic; Classification of observations; The distribution of the sample covariance matrix and the sample generalized variance; Testing the general linear hypothesis; analysis of variance; Testing independence of sets of variates; Testing hypotheses of equality of covariance matrices and equality of mean vectors and covariance matrices; Principal components; Canonical correlation and canonical variables; The distribution of certain characteristic roots and vectors that do not depend on parameters; A review of some other work in multivariate analysis. |
Contents
CHAPTER PAGE | 1 |
CHAPTER PAGE | 4 |
ESTIMATION OF THE MEAN VECTOR AND THE COVARIANCE | 44 |
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A₁ according to N(0 asymptotic B₁ Bayes procedure C. R. Rao Chapter characteristic function characteristic roots columns components compute conditional distribution confidence region consider COROLLARY covariance matrix Cramér defined degrees of freedom distributed according distribution N(0 equation expected value given independently distributed invariant Jacobian joint density joint normal distribution lemma likelihood function likelihood ratio criterion linear combinations marginal distribution maximum likelihood estimate mean vector misclassification multivariate normal distribution N₁ N₂ noncentral nonsingular nonsingular matrix null hypothesis observation obtain orthogonal matrix p₁ parallelotope parameters partial correlation population positive definite probability Problem Proof Prove q₁ r₁ random variables random vector regression S. N. Roy sample correlation Section significance level square statistical testing the hypothesis THEOREM transformation U₁ univariate V₁ variance Wishart distribution X₁ x²-distribution Y₁ Z₁ zero α α στ