Applied Multivariate Statistical AnalysisAspects of mulyivariate analysis; Matrix algebra and random vectors; Sampling geometry and random sampling; The multivariate normal distribution; Inferences about a mean vector; Comparisons of several multivariate means; Multivariate linear regression models; Analysis of covariance structure: principal components; Factor analysis and inference structured covarience matrices; Canonical correlation analysis; Classification and grouping techniques; Discrimination and classification; Clustering. |
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Page 121
... density is a generalization of the univariate normal density to p≥ 2 dimensions . Recall the univariate normal distribution , with mean μ and variance o2 , has the probability density function 1 f ( x ) = e - [ ( x - μ ) / σ ] 2 / 2 ...
... density is a generalization of the univariate normal density to p≥ 2 dimensions . Recall the univariate normal distribution , with mean μ and variance o2 , has the probability density function 1 f ( x ) = e - [ ( x - μ ) / σ ] 2 / 2 ...
Page 123
... density can be written as the product of two univariate normal densities each of the form of ( 4-1 ) . That is , f ... density of a p - dimensional normal variable , it should be clear that the paths of x values yielding a constant ...
... density can be written as the product of two univariate normal densities each of the form of ( 4-1 ) . That is , f ... density of a p - dimensional normal variable , it should be clear that the paths of x values yielding a constant ...
Page 125
... Density ) = We shall obtain the axes of constant probability density contours for a bivariate normal distribution when σ11 = σ22 . From ( 4-7 ) these axes are given by the eigenvalues and eigenvectors of E. Here Σ - XI = 0 becomes 0 ...
... Density ) = We shall obtain the axes of constant probability density contours for a bivariate normal distribution when σ11 = σ22 . From ( 4-7 ) these axes are given by the eigenvalues and eigenvectors of E. Here Σ - XI = 0 becomes 0 ...
Contents
Matrix Algebra and Random Vectors | 35 |
Sample Geometry and Random Sampling | 88 |
35335 | 95 |
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approximately axes calculate canonical correlations canonical variates chi-square chi-square distribution classification clusters confidence intervals confidence region correlation coefficient correlation matrix corresponding cross-products density determined discriminant eigenvalues eigenvectors ellipse ellipsoid Equation error Example Exercise F-distribution factor analysis factor loadings Figure function given H₁ large sample length likelihood ratio likelihood ratio test linear combinations MANOVA maximum likelihood estimates mean vector measurements multivariate normal n₁ n₂ normal distribution normal population observations obtained P₁ pairs parameters population mean Q-Q plots random sample random variables random vector regression model reject residual response Result rotated S₁ sample correlation sample covariance matrix sample mean sample variance scatterplot simultaneous confidence intervals Spooled squared distance statistical sum of squares Table treatment univariate V₁ values X₁ X₂ Y₁ Y₂ Z₁ zero μ₁ μ₂ μι Σ Σ