Methods of multivariate analysis

Praise for the Second Edition "This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight... There is much practical wisdom in this book that is hard to find elsewhere." —IIE Transactions Filled with new and timely content, Metho...

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Hlavní autoři: Rencher, Alvin C., Christensen, William F.
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Hoboken, N.J Wiley 2012
John Wiley & Sons, Incorporated
Wiley-Blackwell
Vydání:3
Edice:Wiley series in probability and statistics
Témata:
Multivariate analysis
ISBN:0470178965, 9780470178966, 1118391659, 9781118391655, 9781118391686, 1118391683
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  • 3.13 DISTANCE BETWEEN VECTORS -- Problems -- 4 The Multivariate Normal Distribution -- 4.1 MULTIVARIATE NORMAL DENSITY FUNCTION -- 4.1.1 Univariate Normal Density -- 4.1.2 Multivariate Normal Density -- 4.1.3 Generalized Population Variance -- 4.1.4 Diversity of Applications of the Multivariate Normal -- 4.2 PROPERTIES OF MULTIVARIATE NORMAL RANDOM VARIABLES -- 4.3 ESTIMATION IN THE MULTIVARIATE NORMAL -- 4.3.1 Maximum Likelihood Estimation -- 4.3.2 Distribution of y and S -- 4.4 ASSESSING MULTIVARIATE NORMALITY -- 4.4.1 Investigating Univariate Normality -- 4.4.2 Investigating Multivariate Normality -- 4.5 TRANSFORMATIONS TO NORMALITY -- 4.5.1 Univariate Transformations to Normality -- 4.5.2 Multivariate Transformations to Normality -- 4.6 OUTLIERS -- 4.6.1 Outliers in Univariate Samples -- 4.6.2 Outliers in Multivariate Samples -- Problems -- 5 Tests on One or Two Mean Vectors -- 5.1 MULTIVARIATE VERSUS UNIVARIATE TESTS -- 5.2 TESTS ON μ WITH Σ KNOWN -- 5.2.1 Review of Univariate Test for H0: μ = μ0 with σ Known -- 5.2.2 Multivariate Test for H0: μ = μ0 with Σ Known -- 5.3 TESTS ON μ WHEN Σ IS UNKNOWN -- 5.3.1 Review of Univariate t-Test for H0: μ = μ0 with σ Unknown -- 5.3.2 Hotelling's T2-Test for H0: μ = μ0 with Σ Unknown -- 5.4 COMPARING TWO MEAN VECTORS -- 5.4.1 Review of Univariate Two-Sample t-Test -- 5.4.2 Multivariate Two-Sample T2 -Test -- 5.4.3 Likelihood Ratio Tests -- 5.5 TESTS ON INDIVIDUAL VARIABLES CONDITIONAL ON REJECTION OF H0 BY THE T2-TEST -- 5.6 COMPUTATION OF T2 -- 5.6.1 Obtaining T2 from a MANOVA Program -- 5.6.2 Obtaining T2 from Multiple Regression -- 5.7 PAIRED OBSERVATIONS TEST -- 5.7.1 Univariate Case -- 5.7.2 Multivariate Case -- 5.8 TEST FOR ADDITIONAL INFORMATION -- 5.9 PROFILE ANALYSIS -- 5.9.1 One-Sample Profile Analysis -- 5.9.2 Two-Sample Profile Analysis -- Problems -- 6 Multivariate Analysis of Variance
  • 7.4 TESTS OF INDEPENDENCE -- 7.4.1 Independence of Two Subvectors -- 7.4.2 Independence of Several Subvectors -- 7.4.3 Test for Independence of All Variables -- Problems -- 8 Discriminant Analysis: Description of Group Separation -- 8.1 INTRODUCTION -- 8.2 THE DISCRIMINANT FUNCTION FOR TWO GROUPS -- 8.3 RELATIONSHIP BETWEEN TWO-GROUP DISCRIMINANT ANALYSIS AND MULTIPLE REGRESSION -- 8.4 DISCRIMINANT ANALYSIS FOR SEVERAL GROUPS -- 8.4.1 Discriminant Functions -- 8.4.2 A Measure of Association for Discriminant Functions -- 8.5 STANDARDIZED DISCRIMINANT FUNCTIONS -- 8.6 TESTS OF SIGNIFICANCE -- 8.6.1 Tests for the Two-Group Case -- 8.6.2 Tests for the Several-Group Case -- 8.7 INTERPRETATION OF DISCRIMINANT FUNCTIONS -- 8.7.1 Standardized Coefficients -- 8.7.2 Partial F-Values -- 8.7.3 Correlations Between Variables and Discriminant Functions -- 8.7.4 Rotation -- 8.8 SCATTERPLOTS -- 8.9 STEPWISE SELECTION OF VARIABLES -- Problems -- 9 Classification Analysis: Allocation of Observations to Groups -- 9.1 INTRODUCTION -- 9.2 CLASSIFICATION INTO TWO GROUPS -- 9.3 CLASSIFICATION INTO SEVERAL GROUPS -- 9.3.1 Equal Population Covariance Matrices: Linear Classification Functions -- 9.3.2 Unequal Population Covariance Matrices: Quadratic Classification Functions -- 9.4 ESTIMATING MISCLASSIFICATION RATES -- 9.5 IMPROVED ESTIMATES OF ERROR RATES -- 9.5.1 Partitioning the Sample -- 9.5.2 Holdout Method -- 9.6 SUBSET SELECTION -- 9.7 NONPARAMETRIC PROCEDURES -- 9.7.1 Multinomial Data -- 9.7.2 Classification Based on Density Estimators -- 9.7.3 Nearest Neighbor Classification Rule -- 9.7.4 Classification Trees -- Problems -- 10 Multivariate Regression -- 10.1 INTRODUCTION -- 10.2 MULTIPLE REGRESSION: FIXED x's -- 10.2.1 Model for Fixed x's -- 10.2.2 Least Squares Estimation in the Fixed-x Model -- 10.2.3 An Estimator for σ2 -- 10.2.4 The Model Corrected for Means
  • 10.2.5 Hypothesis Tests -- 10.2.6 R2 in Fixed-x Regression -- 10.2.7 Subset Selection -- 10.3 MULTIPLE REGRESSION: RANDOM x's -- 10.4 MULTIVARIATE MULTIPLE REGRESSION: ESTIMATION -- 10.4.1 The Multivariate Linear Model -- 10.4.2 Least Squares Estimation in the Multivariate Model -- 10.4.3 Properties of Least Squares Estimator B -- 10.4.4 An Estimator for Σ -- 10.4.5 Model Corrected for Means -- 10.4.6 Estimation in the Seemingly Unrelated Regressions (SUR) Model -- 10.5 MULTIVARIATE MULTIPLE REGRESSION: HYPOTHESIS TESTS -- 10.5.1 Test of Overall Regression -- 10.5.2 Test on a Subset of the x's -- 10.6 MULTIVARIATE MULTIPLE REGRESSION: PREDICTION -- 10.6.1 Confidence Interval for E(y0) -- 10.6.2 Prediction Interval for a Future Observation y0 -- 10.7 MEASURES OF ASSOCIATION BETWEEN THE y's AND THE x's -- 10.8 SUBSET SELECTION -- 10.8.1 Stepwise Procedures -- 10.8.2 All Possible Subsets -- 10.9 MULTIVARIATE REGRESSION: RANDOM x's -- Problems -- 11 Canonical Correlation -- 11.1 INTRODUCTION -- 11.2 CANONICAL CORRELATIONS AND CANONICAL VARIATES -- 11.3 PROPERTIES OF CANONICAL CORRELATIONS -- 11.4 TESTS OF SIGNIFICANCE -- 11.4.1 Tests of No Relationship Between the y's and the x's -- 11.4.2 Test of Significance of Succeeding Canonical Correlations After the First -- 11.5 INTERPRETATION -- 11.5.1 Standardized Coefficients -- 11.5.2 Correlations between Variables and Canonical Variates -- 11.5.3 Rotation -- 11.5.4 Redundancy Analysis -- 11.6 RELATIONSHIPS OF CANONICAL CORRELATION ANALYSIS TO OTHER MULTIVARIATE TECHNIQUES -- 11.6.1 Regression -- 11.6.2 MANOVA and Discriminant Analysis -- Problems -- 12 Principal Component Analysis -- 12.1 INTRODUCTION -- 12.2 GEOMETRIC AND ALGEBRAIC BASES OF PRINCIPAL COMPONENTS -- 12.2.1 Geometric Approach -- 12.2.2 Algebraic Approach -- 12.3 PRINCIPAL COMPONENTS AND PERPENDICULAR REGRESSION
  • 12.4 PLOTTING OF PRINCIPAL COMPONENTS
  • Cover -- Title Page -- Copyright Page -- CONTENTS -- Preface -- Acknowledgments -- 1 Introduction -- 1.1 WHY MULTIVARIATE ANALYSIS? -- 1.2 PREREQUISITES -- 1.3 OBJECTIVES -- 1.4 BASIC TYPES OF DATA AND ANALYSIS -- 2 Matrix Algebra -- 2.1 INTRODUCTION -- 2.2 NOTATION AND BASIC DEFINITIONS -- 2.2.1 Matrices, Vectors, and Scalars -- 2.2.2 Equality of Vectors and Matrices -- 2.2.3 Transpose and Symmetric Matrices -- 2.2.4 Special Matrices -- 2.3 OPERATIONS -- 2.3.1 Summation and Product Notation -- 2.3.2 Addition of Matrices and Vectors -- 2.3.3 Multiplication of Matrices and Vectors -- 2.4 PARTITIONED MATRICES -- 2.5 RANK -- 2.6 INVERSE -- 2.7 POSITIVE DEFINITE MATRICES -- 2.8 DETERMINANTS -- 2.9 TRACE -- 2.10 ORTHOGONAL VECTORS AND MATRICES -- 2.11 EIGENVALUES AND EIGENVECTORS -- 2.11.1 Definition -- 2.11.2 I + A and I - A -- 2.11.3 tr(A)and|A| -- 2.11.4 Positive Definite and Semidefinite Matrices -- 2.11.5 The Product AB -- 2.11.6 Symmetric Matrix -- 2.11.7 Spectral Decomposition -- 2.11.8 Square Root Matrix -- 2.11.9 Square and Inverse Matrices -- 2.11.10 Singular Value Decomposition -- 2.12 KRONECKER AND VEC NOTATION -- Problems -- 3 Characterizing and Displaying Multivariate Data -- 3.1 MEAN AND VARIANCE OF A UNIVARIATE RANDOM VARIABLE -- 3.2 COVARIANCE AND CORRELATION OF BIVARIATE RANDOM VARIABLES -- 3.2.1 Covariance -- 3.2.2 Correlation -- 3.3 SCATTERPLOTS OF BIVARIATE SAMPLES -- 3.4 GRAPHICAL DISPLAYS FOR MULTIVARIATE SAMPLES -- 3.5 DYNAMIC GRAPHICS -- 3.6 MEAN VECTORS -- 3.7 COVARIANCE MATRICES -- 3.8 CORRELATION MATRICES -- 3.9 MEAN VECTORS AND COVARIANCE MATRICES FOR SUBSETS OF VARIABLES -- 3.9.1 Two Subsets -- 3.9.2 Three or More Subsets -- 3.10 LINEAR COMBINATIONS OF VARIABLES -- 3.10.1 Sample Properties -- 3.10.2 Population Properties -- 3.11 MEASURES OF OVERALL VARIABILITY -- 3.12 ESTIMATION OF MISSING VALUES
  • 6.1 ONE-WAY MODELS -- 6.1.1 Univariate One-Way Analysis of Variance (ANOVA) -- 6.1.2 Multivariate One-Way Analysis of Variance Model (MANOVA) -- 6.1.3 Wilks'Test Statistic -- 6.1.4 Roy's Test -- 6.1.5 Pillai and Lawley-Hotelling Tests -- 6.1.6 Unbalanced One-Way MANOVA -- 6.1.7 Summary of the Four Tests and Relationship to T2 -- 6.1.8 Measures of Multivariate Association -- 6.2 COMPARISON OF THE FOUR MANOVA TEST STATISTICS -- 6.3 CONTRASTS -- 6.3.1 Univariate Contrasts -- 6.3.2 Multivariate Contrasts -- 6.4 TESTS ON INDIVIDUAL VARIABLES FOLLOWING REJECTION OF H0 BY THE OVERALL MANOVA TEST -- 6.5 TWO-WAY CLASSIFICATION -- 6.5.1 Review of Univariate Two-Way ANOVA -- 6.5.2 Multivariate Two-Way MANOVA -- 6.6 OTHER MODELS -- 6.6.1 Higher-Order Fixed Effects -- 6.6.2 Mixed Models -- 6.7 CHECKING ON THE ASSUMPTIONS -- 6.8 PROFILE ANALYSIS -- 6.9 REPEATED MEASURES DESIGNS -- 6.9.1 Multivariate Versus Univariate Approach -- 6.9.2 One-Sample Repeated Measures Model -- 6.9.3 κ-Sample Repeated Measures Model -- 6.9.4 Computation of Repeated Measures Tests -- 6.9.5 Repeated Measures with Two Within-Subjects Factors and One Between-Subjects Factor -- 6.9.6 Repeated Measures with Two Within-Subjects Factors and Two Between-Subjects Factors -- 6.9.7 Additional Topics -- 6.10 GROWTH CURVES -- 6.10.1 Growth Curve for One Sample -- 6.10.2 Growth Curves for Several Samples -- 6.10.3 Additional Topics -- 6.11 TESTS ON A SUBVECTOR -- 6.11.1 Test for Additional Information -- 6.11.2 Stepwise Selection of Variables -- Problems -- 7 Tests on Covariance Matrices -- 7.1 INTRODUCTION -- 7.2 TESTING A SPECIFIED PATTERN FOR Σ -- 7.2.1 Testing H0: Σ = Σ0 -- 7.2.2 Testing Sphericity -- 7.2.3 Testing H0: Σ = σ2[(l - ρ)I + ρJ] -- 7.3 TESTS COMPARING COVARIANCE MATRICES -- 7.3.1 Univariate Tests of Equality of Variances -- 7.3.2 Multivariate Tests of Equality of Covariance Matrices