Multivariate observations / G. A. F. Seber.
Series Wiley series in probability and mathematical statisticsProbability and mathematical statisticsEditor: New York : Wiley, c1984Descripción: xx, 686 p. : il. ; 24 cmISBN: 047188104XTema(s): Multivariate analysisOtra clasificación: 62Hxx Recursos en línea: Publisher description1 Preliminaries [1] 1.1 Notation [1] 1.2 What Is Multivariate Analysis? [3] 1.3 Expectation and Covariance Operators [5] 1.4 Sample Data [8] 1.5 Mahalanobis Distances and Angles [10] 1.6 Simultaneous Inference [11] 1.6.1 Simultaneous tests, [11] 1.6.2 Union-intersection principle, [13] 1.7 Likelihood Ratio Tests [14] Exercises 1,14 2 Multivariate Distributions [17] 2.1 Introduction [17] 2.2 Multivariate Normal Distribution [17] 2.3 Wishart Distribution [20] 2.3.1 Definition and properties, [20] 2.3.2 Generalized quadratics, [22] 2.3.3 Noncentral Wishart distribution, [26] 2.3.4 Eigenvalues of a Wishart matrix, [27] 2.3.5 Determinant of a Wishart matrix, [27] 2.4 Hotelling’s T2 Distribution [28] 2.4.1 Central distribution, [28] 2.4.2 Noncentral distribution, [32] 2.5. Multivariate Beta Distributions [32] 2.5.1 Derivation, [32] 2.5.2 Multivariate beta eigenvalues, [35] 2.5.3 Two trace statistics, [38] a. Lawley-Hotelling statistic, [38] b. Pillai’s trace statistic, [39] 2.5.4 U-Distribution, [40] 2.5.5 Summary of special distributions, [42] a. Hotelling’s T2, [42] b. U-statistic, [43] c. Maximum root statistic, [43] d. Trace statistics, [43] e. Equivalence of statistics when mH = 1, [43] 2.5.6 Factorizations of U, [45] a. Product of beta variables, [45] b. Product of two U-statistics, [48] 2.6 Rao’s Distribution [50] 2.7 Multivariate Skewness and Kurtosis [54] Exercises 2, [55] 3 Inference for the Multivariate Normal [59] 3.1 Introduction [59] 3.2 Estimation [59] 3.2.1 Maximum likelihood estimation, [59] 3.2.2 Distribution theory, [63] 3.3 Testing for the Mean [63] 3.3.1 Hotelling’s T2 test, [63] 3.3.2 Power of the test, [69] 3.3.3 Robustness of the test, [69] 3.3.4 Step-down test procedure, [70] 3.4 Linear Constraints on the Mean [71] 3.4.1 Generalization of the paired comparison test, [71] 3.4.2 Some examples, [72] a. Repeated-measurement designs, [72] b. Testing specified contrasts, [76] c. Test for symmetry, [76] d. Testing for a polynomial growth trend, [77] e. Independent estimate of ∑, [77] 3.4.3 Minimization technique for the test statistic, [77] 3.4.4 Confidence intervals, [81] 3.4.5 Functional relationships (errors in variables regression), [85] 3.5 Inference for the Dispersion Matrix [86] 3.5.1 Introduction, [86] 3.5.2 Blockwise independence: Two blocks, [87] a. Likelihood ratio test, [88] b. Maximum root test, [89] 3.5.3 Blockwise independence: b Blocks, [90] 3.5.4 Diagonal dispersion matrix, [92] 3.5.5 Equal diagonal blocks, [94] 3.5.6 Equal correlations and equal variances, [95] 3.5.7 Simultaneous confidence intervals for correlations, [96] 3.5.8 Large-sample inferences, [98] 3.5.9 More general covariance structures, [102] 3.6 Comparing Two Normal Populations [102] 3.6.1 Tests for equal dispersion matrices, [102] a. Likelihood ratio test, [103] b. Union-intersection test, [105] c. Robustness of tests, [106] d. Robust large-sample tests, [107] 3.6.2 Test for equal means assuming equal dispersion matrices, [108] a. Hotelling’s T2 test, [108] b. Effect of unequal dispersion matrices, [111] c. Effect of nonnormality, [112] 3.6.3 Test for equal means assuming unequal dispersion matrices, [114] 3.6.4 Profile analysis: Two populations, [117] Exercises 3, [124] 4 Graphical and Data - Oriented Techniques [127] 4.1 Multivariate Graphical Displays [127] 4.2 Transforming to Normality [138] 4.2.1 Univariate transformations, [138] 4.2.2 Multivariate transformations, [140] 4.3 Distributional Tests and Plots [141] 4.3.1 Investigating marginal distributions, [141] 4.3.2 Tests and plots for multivariate normality, [148] 4.4 Robust Estimation [156] 4.4.1 Why robust estimates?, [156] 4.4.2 Estimation of location, [156] a Univariate methods, [156] b. Multivariate methods, [162] 4.4.3 Estimation of dispersion and covariance, [162] a. Univariate methods, [162] b. Multivariate methods, [165] 4.5 Outlying Observations [169] Exercises 4,173 5 Dimension Reduction and Ordination [175] 5.1 Introduction [175] 5.2 Principal Components [176] 5.2.1 Definition, [176] 5.2.2 Dimension reduction properties, [176] 5.2.3 Further properties, [181] 5.2.4 Sample principal components, [184] 5.2.5 Inference for sample components, [197] 5.2.6 Preliminary selection of variables, [200] 5.2.7 General applications, [200] 5.2.8 Generalized principal components analysis, [203] 5.3- Biplots and A-Plots [204] 5.4 Factor Analysis [213] 5.4.1 Underlying model, [213] 5.4.2 Estimation procedures, [216] a. Method of maximum likelihood, [216] b. Principal factor analysis, [219] c. Estimating factor scores, [220] 5.4.3 Some difficulties, [222] a. Principal factor analysis, [225] b. Maximum likelihood factor analysis, [230] c. Conclusions, [231] 5.5 Multidimensional Scaling [235] 5.5.1 Classical (metric) solution, [235] 5.5.2 Nonmetric scaling, [241] 5.6 Procrustes Analysis (Matching Configurations) [253] 5.7 Canonical Correlations and Variates [256] 5.7.1 Population correlations, [256] 5.7.2 Sample canonical correlations, [260] 5.7.3 Inference, [264] 5.7.4 More than two sets of variables, [267] 5.8 Discriminant Coordinates [269] 5.9 Assessing Two-Dimensional Representations [273] 5.10 A Brief Comparison of Methods [274] Exercises 5, [275] 6 Discriminant Analysis [279] 6.1 Introduction [279] 6.2 Two Groups: Known Distributions [280] 6.2.1 Misclassification errors, [280] 6.2.2 Some allocation principles, [281] a. Minimize total probability of misclassification, [281] b. Likelihood ratio method, [285] c. Minimize total cost of misclassification, [285] d. Maximize the posterior probability, [285] e. Minimax allocation, [286] f. Summary, [287] 6.3 Two Groups: Known Distributions With Unknown Parameters [287] 6.3.1 General methods, [287] 6.3.2 Normal populations, [293] a. Linear discriminant function, [293] b. Quadratic discriminant function, [297] c. Robustness of LDF and QDF, [297] d. Missing values, [300] e. Predictive discriminant, [301] 6.3.3 Multivariate discrete distributions, [303] a. Independent binary variables, [303] b. Correlated binary variables, [304] c. Correlated discrete variables, [306] 6.3.4 Multivariate discrete-continuous distributions, [306] 6.4 Two Groups: Logistic Discriminant [308] 6.4.1 General model, [308] 6.4.2 Sampling designs, [309] a. Conditional sampling, [309] b. Mixture sampling, [310] c. Separate sampling, [310] 6.4.3 Computations, [312] 6.4.4 LGD versus LDF, [317] 6.4.5 Predictive logistic model, [318] 6.4.6 Quadratic discrimination, [319] 6.5 Two Groups: Unknown Distributions [320] 6.5.1 Kernel method, [320] a. Continuous data, [320] b. Binary data, [322] c. Continuous and discrete data, [323] 6.5.2 Other nonparametric methods, [323] a Nearest neighbor techniques, [323] b. Partitioning methods, [324] c. Distance methods, [324] d. Rank procedures, [324] e. Sequential discrimination on the variables, [326] 6.6 Utilizing Unclassified Observations [327] 6.7 All Observations Unclassified (Method of Mixtures) [328] 6.8 Cases of Doubt [329] 6.9 More Than Two Groups [330] 6.10 Selection of Variables [337] 6.10.1 Two groups, [337] 6.10.2 More than two groups, [341] 6.11 Some Conclusions [342] Exercises 6, [343]
7 Cluster Analysis [347] 7.1 Introduction [347] 7.2 Proximity data [351] 7.2.1 Dissimilarities, [351] 7.2.2 Similarities, [356] 7.3 Hierarchical Clustering: Agglomerative Techniques [359] 7.3.1 Some commonly used methods, [360] a. Single linkage (nearest neighbor) method, [360] b. Complete linkage (farthest neighbor) method, [361] c. Centroid method, [362] d. Incremental sum of squares method, [363] e. Median method, [363] f. Group average method, [363] g. Lance and Williams flexible method, [364] h. Information measures, [365] i. Other methods, [366] 7.3.2 Comparison of methods, [368] a. Monotonicity, [368] b. Spatial properties, [373] c. Computational effort, [375] 7.4 Hierarchical Clustering: Divisive Techniques [376] 7.4.1 Monothetic methods, [377] 7.4.2 Polythetic methods, [378] 7.5. Partitioning Methods [379] 7.5.1 Number of partitions, [379] 7.5.2 Starting the process, [379] 7.5.3 Reassigning the objects, [380] a. Minimize trace W, [382] b. Minimize | W|, [382] c. Maximize trace BW-1 [383] 7.5.4 Other techniques, [386] 7.6 Overlapping Clusters (Clumping) [387] 7.7 Choosing the Number of Clusters [388] 7.8 General Comments [390] Exercises 7, [392] 8 Multivariate Linear Models [395] 8.1 Least Squares Estimation [395] 8.2 Properties of Least Squares Estimates [399] g,3 Least Squares With Linear Constraints [403] 8.4 Distribution Theory [405] g.5 Analysis of Residuals [408] 8.6 Hypothesis Testing [409] 8.6.1 Extension of univariate theory, [409] 8.6.2 Test procedures, [411] a. Union-intersection test, [411] b. Likelihood ratio test, [412] c. Other test statistics, [413] d. Comparison of four test statistics, [414] e. Mardia’s permutation test, [416] 8.6.3 Simultaneous confidence intervals, [417] 8.6.4 Comparing two populations, [419] 8.6.5 Canonical form, [421] 8.6.6 Missing observations, [422] 8.6.7 Other topics, [423] 8.7 A Generalized Linear Hypothesis [423] 8.7.1 Theory, [423] 8.7.2 Profile analysis for K populations, [424] 8.7.3 Tests for mean of multivariate normal, [425] 8.8 Step-Down Procedures [426] 8.9 Multiple Design Models [428] Exercises 8, [431] 9 Multivariate Analysis of Variance and Covariance [433] Introduction [433] One-Way Classification [433] 9.2.1 Hypothesis testing, [433] 9.2.2 Multiple comparisons, [437] 9.2.3 Comparison of test statistics, [440] 9.2.4 Robust tests for equal means, [443] a. Permutation test, [443] b. James’ test, [445] 9.2.5 Reparameterization, [447] 9.2.6 Comparing dispersion matrices, [448] a. Test for equal dispersion matrices, [448] b. Graphical comparisons, [451] 9.2.7 Exact procedures for means assuming unequal dispersion matrices, [452] a. Hypothesis testing, [452] b. Multiple confidence intervals, [454] Randomized Block Design [454] 9.3.1 Hypothesis testing and confidence intervals, [454] 9.3.2 Underlying assumptions, [458] 9.4 Two-Way Classification With Equal Observations per Mean [458] 9.5 Analysis of Covariance [463] 9.5.1 Univariate theory, [463] 9.5.2 Multivariate theory, [465] 9.5.3 Test for additional information, [471] 9.6 Multivariate Cochran’s Theorem on Quadratics [472] 9.7 Growth Curve Analysis [474] 9.7.1 Examples, [474] a. Single growth curve, [474] b. Two growth curves, [475] c. Single growth curve for a randomized block design, [476] d. Two-dimensional growth curve, [477] 9.7.2 General theory, [478] a. Potthoff and Roy’s method, [479] b. Rao-Khatri analysis of covariance method, [480] c. Choice of method, [483] 9.7.3 Single growth curve, [484] 9.7.4 Test for internal adequacy, [486] 9.7.5 A case study, [487] 9.7.6 Further topics, [492] Exercises 9, [494] 10 Special Topics [496] 10.1 Computational Techniques [496] 10.1.1 Solving the normal equations, [496] a. Cholesky decomposition, [496] b. QR-algorithm, [497] 10.1.2 Hypothesis matrix, [498] 10.1.3 Calculating Hotelling's T2, [499] 10.1.4 Generalized symmetric eigenproblem, [500] a. Multivariate linear hypothesis, [501] b. One-way classification, [503] c. Discriminant coordinates, [504] 10.1.5 Singular value decomposition, [504] a. Definition, [504] b. Solution of normal equations, [505] c. Principal components, [506] d. Canonical correlations, [506] 10.1.6 Selecting the best subset, [507] a. Response variables, [507] b. Regressor variables, [510] 10.2 Log-Linear Models for Binary Data [512] 10.3 Incomplete Data [514] appendix [517] A Some Matrix Algebra [517] Al Trace and eigenvalues, [517] A2 Rank, [518] A3 Patterned matrices, [519] A4 Positive semidefinite matrices, [521] A5 Positive definite matrices, [521] A6 Idempotent matrices, [522] A7 Optimization and inequalities, [523] A8 Vector and matrix differentiation, [530] A9 Jacobians and transformations, [531] A10 Asymptotic normality, [532] B Orthogonal Projections [533] Bl Orthogonal decomposition of vectors, [533] B2 Orthogonal complements, [534] B3 Projections on subspaces, [535] C Order Statistics and Probability Plotting [539] Cl Sample distribution functions, [539] C2 Gamma distribution, [540] C3 Beta distribution, [541] C4 Probability plotting, [542] D Statistical Tables [545] DI Bonferroni t-percentage points, [546] D2 Maximum likelihood estimates for the gamma distribution, [550] D3 Upper tail percentage points for √b1, [551] D4 Coefficients in a normalizing transformation of √b1, [551] D5 Simulation percentiles for b2, [553] D6 Charts for the percentiles of b2, [554] D7 Coefficients for the Wilk-Shapiro (W) test, [556] D8 Percentiles for the Wilk-Shapiro (W) test, [558] D9 DAgostino's test for normality, [558] D10 Anderson-Darling (A2n) test for normality, [560] Dll Discordancy test for single gamma outlier, [561] DI2 Discordancy test for single multivariate normal outlier, [562] DI3 Wilks9 likelihood ratio test, [562] D14 Roy’s maximum root statistic, [563] DI5 Law ley-Hotelling trace statistic, [563] D16 Pillai’s trace statistic, [564] DI 7 Test for mutual independence, [564] DI 8 Test for equal dispersion matrices with equal sample sizes, [564] Outline Solutions to Exercises [615] References [626] Index [671]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Incluye referencias bibliográficas (p. 626-670) e índice.
1 Preliminaries [1] --
1.1 Notation [1] --
1.2 What Is Multivariate Analysis? [3] --
1.3 Expectation and Covariance Operators [5] --
1.4 Sample Data [8] --
1.5 Mahalanobis Distances and Angles [10] --
1.6 Simultaneous Inference [11] --
1.6.1 Simultaneous tests, [11] --
1.6.2 Union-intersection principle, [13] --
1.7 Likelihood Ratio Tests [14] --
Exercises 1,14 --
2 Multivariate Distributions [17] --
2.1 Introduction [17] --
2.2 Multivariate Normal Distribution [17] --
2.3 Wishart Distribution [20] --
2.3.1 Definition and properties, [20] --
2.3.2 Generalized quadratics, [22] --
2.3.3 Noncentral Wishart distribution, [26] --
2.3.4 Eigenvalues of a Wishart matrix, [27] --
2.3.5 Determinant of a Wishart matrix, [27] --
2.4 Hotelling’s T2 Distribution [28] --
2.4.1 Central distribution, [28] --
2.4.2 Noncentral distribution, [32] --
2.5. Multivariate Beta Distributions [32] --
2.5.1 Derivation, [32] --
2.5.2 Multivariate beta eigenvalues, [35] --
2.5.3 Two trace statistics, [38] --
a. Lawley-Hotelling statistic, [38] --
b. Pillai’s trace statistic, [39] --
2.5.4 U-Distribution, [40] --
2.5.5 Summary of special distributions, [42] --
a. Hotelling’s T2, [42] --
b. U-statistic, [43] --
c. Maximum root statistic, [43] --
d. Trace statistics, [43] --
e. Equivalence of statistics when mH = 1, [43] --
2.5.6 Factorizations of U, [45] --
a. Product of beta variables, [45] --
b. Product of two U-statistics, [48] --
2.6 Rao’s Distribution [50] --
2.7 Multivariate Skewness and Kurtosis [54] --
Exercises 2, [55] --
3 Inference for the Multivariate Normal [59] --
3.1 Introduction [59] --
3.2 Estimation [59] --
3.2.1 Maximum likelihood estimation, [59] --
3.2.2 Distribution theory, [63] --
3.3 Testing for the Mean [63] --
3.3.1 Hotelling’s T2 test, [63] --
3.3.2 Power of the test, [69] --
3.3.3 Robustness of the test, [69] --
3.3.4 Step-down test procedure, [70] --
3.4 Linear Constraints on the Mean [71] --
3.4.1 Generalization of the paired comparison test, [71] --
3.4.2 Some examples, [72] --
a. Repeated-measurement designs, [72] --
b. Testing specified contrasts, [76] --
c. Test for symmetry, [76] --
d. Testing for a polynomial growth trend, [77] --
e. Independent estimate of ∑, [77] --
3.4.3 Minimization technique for the test statistic, [77] --
3.4.4 Confidence intervals, [81] --
3.4.5 Functional relationships (errors in variables regression), [85] --
3.5 Inference for the Dispersion Matrix [86] --
3.5.1 Introduction, [86] --
3.5.2 Blockwise independence: Two blocks, [87] --
a. Likelihood ratio test, [88] --
b. Maximum root test, [89] --
3.5.3 Blockwise independence: b Blocks, [90] --
3.5.4 Diagonal dispersion matrix, [92] --
3.5.5 Equal diagonal blocks, [94] --
3.5.6 Equal correlations and equal variances, [95] --
3.5.7 Simultaneous confidence intervals for correlations, [96] --
3.5.8 Large-sample inferences, [98] --
3.5.9 More general covariance structures, [102] --
3.6 Comparing Two Normal Populations [102] --
3.6.1 Tests for equal dispersion matrices, [102] --
a. Likelihood ratio test, [103] --
b. Union-intersection test, [105] --
c. Robustness of tests, [106] --
d. Robust large-sample tests, [107] --
3.6.2 Test for equal means assuming equal dispersion matrices, [108] --
a. Hotelling’s T2 test, [108] --
b. Effect of unequal dispersion matrices, [111] --
c. Effect of nonnormality, [112] --
3.6.3 Test for equal means assuming unequal dispersion matrices, [114] --
3.6.4 Profile analysis: Two populations, [117] --
Exercises 3, [124] --
4 Graphical and Data - Oriented Techniques [127] --
4.1 Multivariate Graphical Displays [127] --
4.2 Transforming to Normality [138] --
4.2.1 Univariate transformations, [138] --
4.2.2 Multivariate transformations, [140] --
4.3 Distributional Tests and Plots [141] --
4.3.1 Investigating marginal distributions, [141] --
4.3.2 Tests and plots for multivariate normality, [148] --
4.4 Robust Estimation [156] --
4.4.1 Why robust estimates?, [156] --
4.4.2 Estimation of location, [156] --
a Univariate methods, [156] --
b. Multivariate methods, [162] --
4.4.3 Estimation of dispersion and covariance, [162] --
a. Univariate methods, [162] --
b. Multivariate methods, [165] --
4.5 Outlying Observations [169] --
Exercises 4,173 --
5 Dimension Reduction and Ordination [175] --
5.1 Introduction [175] --
5.2 Principal Components [176] --
5.2.1 Definition, [176] --
5.2.2 Dimension reduction properties, [176] --
5.2.3 Further properties, [181] --
5.2.4 Sample principal components, [184] --
5.2.5 Inference for sample components, [197] --
5.2.6 Preliminary selection of variables, [200] --
5.2.7 General applications, [200] --
5.2.8 Generalized principal components analysis, [203] --
5.3- Biplots and A-Plots [204] --
5.4 Factor Analysis [213] --
5.4.1 Underlying model, [213] --
5.4.2 Estimation procedures, [216] --
a. Method of maximum likelihood, [216] --
b. Principal factor analysis, [219] --
c. Estimating factor scores, [220] --
5.4.3 Some difficulties, [222] --
a. Principal factor analysis, [225] --
b. Maximum likelihood factor analysis, [230] --
c. Conclusions, [231] --
5.5 Multidimensional Scaling [235] --
5.5.1 Classical (metric) solution, [235] --
5.5.2 Nonmetric scaling, [241] --
5.6 Procrustes Analysis (Matching Configurations) [253] --
5.7 Canonical Correlations and Variates [256] --
5.7.1 Population correlations, [256] --
5.7.2 Sample canonical correlations, [260] --
5.7.3 Inference, [264] --
5.7.4 More than two sets of variables, [267] --
5.8 Discriminant Coordinates [269] --
5.9 Assessing Two-Dimensional Representations [273] --
5.10 A Brief Comparison of Methods [274] --
Exercises 5, [275] --
6 Discriminant Analysis [279] --
6.1 Introduction [279] --
6.2 Two Groups: Known Distributions [280] --
6.2.1 Misclassification errors, [280] --
6.2.2 Some allocation principles, [281] --
a. Minimize total probability of misclassification, [281] --
b. Likelihood ratio method, [285] --
c. Minimize total cost of misclassification, [285] --
d. Maximize the posterior probability, [285] --
e. Minimax allocation, [286] --
f. Summary, [287] --
6.3 Two Groups: Known Distributions With Unknown Parameters [287] --
6.3.1 General methods, [287] --
6.3.2 Normal populations, [293] --
a. Linear discriminant function, [293] --
b. Quadratic discriminant function, [297] --
c. Robustness of LDF and QDF, [297] --
d. Missing values, [300] --
e. Predictive discriminant, [301] --
6.3.3 Multivariate discrete distributions, [303] --
a. Independent binary variables, [303] --
b. Correlated binary variables, [304] --
c. Correlated discrete variables, [306] --
6.3.4 Multivariate discrete-continuous distributions, [306] --
6.4 Two Groups: Logistic Discriminant [308] --
6.4.1 General model, [308] --
6.4.2 Sampling designs, [309] --
a. Conditional sampling, [309] --
b. Mixture sampling, [310] --
c. Separate sampling, [310] --
6.4.3 Computations, [312] --
6.4.4 LGD versus LDF, [317] --
6.4.5 Predictive logistic model, [318] --
6.4.6 Quadratic discrimination, [319] --
6.5 Two Groups: Unknown Distributions [320] --
6.5.1 Kernel method, [320] --
a. Continuous data, [320] --
b. Binary data, [322] --
c. Continuous and discrete data, [323] --
6.5.2 Other nonparametric methods, [323] --
a Nearest neighbor techniques, [323] --
b. Partitioning methods, [324] --
c. Distance methods, [324] --
d. Rank procedures, [324] --
e. Sequential discrimination on the variables, [326] --
6.6 Utilizing Unclassified Observations [327] --
6.7 All Observations Unclassified (Method of Mixtures) [328] --
6.8 Cases of Doubt [329] --
6.9 More Than Two Groups [330] --
6.10 Selection of Variables [337] --
6.10.1 Two groups, [337] --
6.10.2 More than two groups, [341] --
6.11 Some Conclusions [342] --
Exercises 6, [343] --
7 Cluster Analysis [347] --
7.1 Introduction [347] --
7.2 Proximity data [351] --
7.2.1 Dissimilarities, [351] --
7.2.2 Similarities, [356] --
7.3 Hierarchical Clustering: Agglomerative Techniques [359] --
7.3.1 Some commonly used methods, [360] --
a. Single linkage (nearest neighbor) method, [360] --
b. Complete linkage (farthest neighbor) method, [361] --
c. Centroid method, [362] --
d. Incremental sum of squares method, [363] --
e. Median method, [363] --
f. Group average method, [363] --
g. Lance and Williams flexible method, [364] --
h. Information measures, [365] --
i. Other methods, [366] --
7.3.2 Comparison of methods, [368] --
a. Monotonicity, [368] --
b. Spatial properties, [373] --
c. Computational effort, [375] --
7.4 Hierarchical Clustering: Divisive Techniques [376] --
7.4.1 Monothetic methods, [377] --
7.4.2 Polythetic methods, [378] --
7.5. Partitioning Methods [379] --
7.5.1 Number of partitions, [379] --
7.5.2 Starting the process, [379] --
7.5.3 Reassigning the objects, [380] --
a. Minimize trace W, [382] --
b. Minimize | W|, [382] --
c. Maximize trace BW-1 [383] --
7.5.4 Other techniques, [386] --
7.6 Overlapping Clusters (Clumping) [387] --
7.7 Choosing the Number of Clusters [388] --
7.8 General Comments [390] --
Exercises 7, [392] --
8 Multivariate Linear Models [395] --
8.1 Least Squares Estimation [395] --
8.2 Properties of Least Squares Estimates [399] --
g,3 Least Squares With Linear Constraints [403] --
8.4 Distribution Theory [405] --
g.5 Analysis of Residuals [408] --
8.6 Hypothesis Testing [409] --
8.6.1 Extension of univariate theory, [409] --
8.6.2 Test procedures, [411] --
a. Union-intersection test, [411] --
b. Likelihood ratio test, [412] --
c. Other test statistics, [413] --
d. Comparison of four test statistics, [414] --
e. Mardia’s permutation test, [416] --
8.6.3 Simultaneous confidence intervals, [417] --
8.6.4 Comparing two populations, [419] --
8.6.5 Canonical form, [421] --
8.6.6 Missing observations, [422] --
8.6.7 Other topics, [423] --
8.7 A Generalized Linear Hypothesis [423] --
8.7.1 Theory, [423] --
8.7.2 Profile analysis for K populations, [424] --
8.7.3 Tests for mean of multivariate normal, [425] --
8.8 Step-Down Procedures [426] --
8.9 Multiple Design Models [428] --
Exercises 8, [431] --
9 Multivariate Analysis of Variance and Covariance [433] --
Introduction [433] --
One-Way Classification [433] --
9.2.1 Hypothesis testing, [433] --
9.2.2 Multiple comparisons, [437] --
9.2.3 Comparison of test statistics, [440] --
9.2.4 Robust tests for equal means, [443] --
a. Permutation test, [443] --
b. James’ test, [445] --
9.2.5 Reparameterization, [447] --
9.2.6 Comparing dispersion matrices, [448] --
a. Test for equal dispersion matrices, [448] --
b. Graphical comparisons, [451] --
9.2.7 Exact procedures for means assuming unequal dispersion matrices, [452] --
a. Hypothesis testing, [452] --
b. Multiple confidence intervals, [454] --
Randomized Block Design [454] --
9.3.1 Hypothesis testing and confidence intervals, [454] --
9.3.2 Underlying assumptions, [458] --
9.4 Two-Way Classification With Equal Observations per Mean [458] --
9.5 Analysis of Covariance [463] --
9.5.1 Univariate theory, [463] --
9.5.2 Multivariate theory, [465] --
9.5.3 Test for additional information, [471] --
9.6 Multivariate Cochran’s Theorem on Quadratics [472] --
9.7 Growth Curve Analysis [474] --
9.7.1 Examples, [474] --
a. Single growth curve, [474] --
b. Two growth curves, [475] --
c. Single growth curve for a randomized block design, [476] --
d. Two-dimensional growth curve, [477] --
9.7.2 General theory, [478] --
a. Potthoff and Roy’s method, [479] --
b. Rao-Khatri analysis of covariance method, [480] --
c. Choice of method, [483] --
9.7.3 Single growth curve, [484] --
9.7.4 Test for internal adequacy, [486] --
9.7.5 A case study, [487] --
9.7.6 Further topics, [492] --
Exercises 9, [494] --
10 Special Topics [496] --
10.1 Computational Techniques [496] --
10.1.1 Solving the normal equations, [496] --
a. Cholesky decomposition, [496] --
b. QR-algorithm, [497] --
10.1.2 Hypothesis matrix, [498] --
10.1.3 Calculating Hotelling's T2, [499] --
10.1.4 Generalized symmetric eigenproblem, [500] --
a. Multivariate linear hypothesis, [501] --
b. One-way classification, [503] --
c. Discriminant coordinates, [504] --
10.1.5 Singular value decomposition, [504] --
a. Definition, [504] --
b. Solution of normal equations, [505] --
c. Principal components, [506] --
d. Canonical correlations, [506] --
10.1.6 Selecting the best subset, [507] --
a. Response variables, [507] --
b. Regressor variables, [510] --
10.2 Log-Linear Models for Binary Data [512] --
10.3 Incomplete Data [514] --
appendix [517] --
A Some Matrix Algebra [517] --
Al Trace and eigenvalues, [517] --
A2 Rank, [518] --
A3 Patterned matrices, [519] --
A4 Positive semidefinite matrices, [521] --
A5 Positive definite matrices, [521] --
A6 Idempotent matrices, [522] --
A7 Optimization and inequalities, [523] --
A8 Vector and matrix differentiation, [530] --
A9 Jacobians and transformations, [531] --
A10 Asymptotic normality, [532] --
B Orthogonal Projections [533] --
Bl Orthogonal decomposition of vectors, [533] --
B2 Orthogonal complements, [534] --
B3 Projections on subspaces, [535] --
C Order Statistics and Probability Plotting [539] --
Cl Sample distribution functions, [539] --
C2 Gamma distribution, [540] --
C3 Beta distribution, [541] --
C4 Probability plotting, [542] --
D Statistical Tables [545] --
DI Bonferroni t-percentage points, [546] --
D2 Maximum likelihood estimates for the gamma distribution, [550] --
D3 Upper tail percentage points for √b1, [551] --
D4 Coefficients in a normalizing transformation of √b1, [551] --
D5 Simulation percentiles for b2, [553] --
D6 Charts for the percentiles of b2, [554] --
D7 Coefficients for the Wilk-Shapiro (W) test, [556] --
D8 Percentiles for the Wilk-Shapiro (W) test, [558] --
D9 DAgostino's test for normality, [558] --
D10 Anderson-Darling (A2n) test for normality, [560] --
Dll Discordancy test for single gamma outlier, [561] --
DI2 Discordancy test for single multivariate normal outlier, [562] --
DI3 Wilks9 likelihood ratio test, [562] --
D14 Roy’s maximum root statistic, [563] --
DI5 Law ley-Hotelling trace statistic, [563] --
D16 Pillai’s trace statistic, [564] --
DI 7 Test for mutual independence, [564] --
DI 8 Test for equal dispersion matrices with equal sample sizes, [564] --
Outline Solutions to Exercises [615] --
References [626] --
Index [671] --
MR, 86f:62080
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