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 144
Richard Arnold Johnson, Dean W. Wichern. 4.5 LARGE - SAMPLE BEHAVIOR OF X AND S Suppose the quantity X is determined by a large number of independent causes , V1 , V2 , ... , Vn , where the random variables V ,, representing the causes ...
Richard Arnold Johnson, Dean W. Wichern. 4.5 LARGE - SAMPLE BEHAVIOR OF X AND S Suppose the quantity X is determined by a large number of independent causes , V1 , V2 , ... , Vn , where the random variables V ,, representing the causes ...
Page 190
... LARGE - SAMPLE INFERENCES ABOUT A POPULATION MEAN VECTOR When the sample size is large , tests of hypotheses and confidence regions for μ can be constructed without the assumption of a normal population . As illustrated more fully by ...
... LARGE - SAMPLE INFERENCES ABOUT A POPULATION MEAN VECTOR When the sample size is large , tests of hypotheses and confidence regions for μ can be constructed without the assumption of a normal population . As illustrated more fully by ...
Page 461
... with the factor n - 1 ( p + q + 1 ) to improve the x2 approximation to the sampling distribution of -2 In A. Thus for n and n ( p + q ) large , we - - Reject Ho : 12 = 0 ( p * = Sec . 10.6 461 Large - Sample Inferences Large-Sample ...
... with the factor n - 1 ( p + q + 1 ) to improve the x2 approximation to the sampling distribution of -2 In A. Thus for n and n ( p + q ) large , we - - Reject Ho : 12 = 0 ( p * = Sec . 10.6 461 Large - Sample Inferences Large-Sample ...
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