| Description |
1 online resource |
| Series |
Wiley series in probability and statistics |
| Contents |
880-01 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 |
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880-01/(S 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 ∑ 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 |
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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 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 |
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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 -- 3.13. DISTANCE BETWEEN VECTORS -- Problems |
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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 |
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5.4. COMPARING TWO MEAN VECTORS |
| Summary |
"This new edition, now with a co-author, offers a complete and up-to-date examination of the field. The authors have streamlined previously tedious topics, such as multivariate regression and MANOVA techniques, to add newer, more timely content. Each chapter contains exercises, providing readers with the opportunity to test and extend their understanding. The new edition also presents several expanded topics in Kronecker product; prediction errors; maximum likelihood estimation; and selective key, but accessible proofs. This resource meets the needs of both statistics majors and those of students and professionals in other fields"-- Provided by publisher |
| Notes |
Includes index |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record and CIP data provided by publisher |
| Subject |
Multivariate analysis.
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Multivariate Analysis
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MATHEMATICS -- Probability & Statistics -- Multivariate Analysis.
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Multivariate analysis
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Anàlisi multivariable.
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| Genre/Form |
Llibres electrònics.
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| Form |
Electronic book
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| Author |
Christensen, William F., 1970-
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| LC no. |
2012009959 |
| ISBN |
9781118391679 |
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1118391675 |
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9781118391655 |
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1118391659 |
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9781118391662 |
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1118391667 |
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9781118391686 |
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1118391683 |
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9781282241886 |
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1282241885 |
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