Normal view

## 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 description
Contenidos:
```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]
2.3.3 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]
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]
6.5 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]
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
Libros
Libros ordenados por tema 62 Se443m (Browse shelf) Available A-5943

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] --
2.3.3 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] --
6.5 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] --
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

There are no comments on this title.