Multivariate statistical analysis /

Multivariate statistical analysis /

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Bibliographic Details
Author / Creator:Giri, Narayan C., 1928-
Edition:2nd ed., rev. and expanded.
Imprint:New York : Marcel Dekker, c2004.
Description:xiv, 558 p. : ill. ; 24 cm.
Language:English
Series:Statistics, textbooks and monographs ; 171
Statistics, textbooks and monographs ; v. 171.
Subject:
Multivariate analysis.
Multivariate analysis.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/5050152
Hidden Bibliographic Details
ISBN:0824747135 (acid-free paper)
Notes:Includes bibliographical references (p. 529-530) and indexes.
Table of Contents:
  • Preface to the Second Edition
  • Preface to the First Edition
  • 1. Vector and Matrix Algebra
  • 1.0. Introduction
  • 1.1. Vectors
  • 1.2. Matrices
  • 1.3. Rank and Trace of a Matrix
  • 1.4. Quadratic Forms and Positive Definite Matrix
  • 1.5. Characteristic Roots and Vectors
  • 1.6. Partitioned Matrix
  • 1.7. Some Special Theorems on Matrix Derivatives
  • 1.8. Complex Matrices
  • Exercises
  • References
  • 2. Groups, Jacobian of Some Transformations, Functions and Spaces
  • 2.0. Introduction
  • 2.1. Groups
  • 2.2. Some Examples of Groups
  • 2.3. Quotient Group, Homomorphism, Isomorphism
  • 2.4. Jacobian of Some Transformations
  • 2.5. Functions and Spaces
  • References
  • 3. Multivariate distributions and Invariance
  • 3.0. Introduction
  • 3.1. Multivariate Distributions
  • 3.2. Invariance in Statistical Testing of Hypotheses
  • 3.3. Almost Invariance and Invariance
  • 3.4. Sufficiency and Invariance
  • 3.5. Unbiasedness and Invariance
  • 3.6. Invariance and Optimum Tests
  • 3.7. Most Stringent Tests and Invariance
  • 3.8. Locally Best and Uniformly Most Powerful Invariant Tests
  • 3.9. Ratio of Distributions of Maximal Invariant, Stein's Theorem
  • 3.10. Derivation of Locally Best Invariant Tests (LBI)
  • Exercises
  • References
  • 4. Properties of Multivariate Distributions
  • 4.0. Introduction
  • 4.1. Multivariate Normal Distribution (Classical Approach)
  • 4.2. Complex Multivariate Normal Distribution
  • 4.3. Symmetric Distribution: Its Properties and Characterizations
  • 4.4. Concentration Ellipsoid and Axes (Multivariate Normal)
  • 4.5. Regression, Multiple and Partial Correlation
  • 4.6. Cumulants and Kurtosis
  • 4.7. The Redundancy Index
  • Exercises
  • References
  • 5. Estimators of Parameters and Their Functions
  • 5.0. Introduction
  • 5.1. Maximum Likelihood Estimators of [mu], [Sigma] in N[subscript p]([mu], [Sigma])
  • 5.2. Classical Properties of Maximum Likelihood Estimators
  • 5.3. Bayes, Minimax, and Admissible Characters
  • 5.4. Equivariant Estimation Under Curved Models
  • Exercises
  • References
  • 6. Basic Multivariate Sampling Distributions
  • 6.0. Introduction
  • 6.1. Noncentral Chi-Square, Student's t-, F-Distributions
  • 6.2. Distribution of Quadratic Forms
  • 6.3. The Wishart Distribution
  • 6.4. Properties of the Wishart Distribution
  • 6.5. The Noncentral Wishart Distribution
  • 6.6. Generalized Variance
  • 6.7. Distribution of the Bartlett Decomposition (Rectangular Coordinates)
  • 6.8. Distribution of Hotelling's T[superscript 2]
  • 6.9. Multiple and Partial Correlation Coefficients
  • 6.10. Distribution of Multiple Partial Correlation Coefficients
  • 6.11. Basic Distributions in Multivariate Complex Normal
  • 6.12. Basic Distributions in Symmetrical Distributions
  • Exercises
  • References
  • 7. Tests of Hypotheses of Mean Vectors
  • 7.0. Introduction
  • 7.1. Tests: Known Covariances
  • 7.2. Tests: Unknown Covariances
  • 7.3. Tests of Subvectors of [mu] in Multivariate Normal
  • 7.4. Tests of Mean Vector in Complex Normal
  • 7.5. Tests of Means in Symmetric Distributions
  • Exercises
  • References
  • 8. Tests Concerning Covariance Matrices and Mean Vectors
  • 8.0. Introduction
  • 8.1. Hypothesis: A Covariance Matrix Is Unknown
  • 8.2. The Sphericity Test
  • 8.3. Tests of Independence and the R[superscript 2]-Test
  • 8.4. Admissibility of the Test of Independence and the R[superscript 2]-Test
  • 8.5. Minimax Character of the R[superscript 2]-Test
  • 8.6. Multivariate General Linear Hypothesis
  • 8.7. Equality of Several Covariance Matrices
  • 8.8. Complex Analog of R[superscript 2]-Test
  • 8.9. Tests of Scale Matrices in E[subscript p]([mu], [Sigma])
  • 8.10. Tests with Missing Data
  • Exercises
  • References
  • 9. Discriminant Analysis
  • 9.0. Introduction
  • 9.1. Examples
  • 9.2. Formulation of the Problem of Discriminant Analysis
  • 9.3. Classification into One of Two Multivariate Normals
  • 9.4. Classification into More than Two Multivariate Normals
  • 9.5. Concluding Remarks
  • 9.6. Discriminant Analysis and Cluster Analysis
  • Exercises
  • References
  • 10. Principal Components
  • 10.0. Introduction
  • 10.1. Principal Components
  • 10.2. Population Principal Components
  • 10.3. Sample Principal Components
  • 10.4. Example
  • 10.5. Distribution of Characteristic Roots
  • 10.6. Testing in Principal Components
  • Exercises
  • References
  • 11. Canonical Correlations
  • 11.0. Introduction
  • 11.1. Population Canonical Correlations
  • 11.2. Sample Canonical Correlations
  • 11.3. Tests of Hypotheses
  • Exercises
  • References
  • 12. Factor Analysis
  • 12.0. Introduction
  • 12.1. Orthogonal Factor Model
  • 12.2. Oblique Factor Model
  • 12.3. Estimation of Factor Loadings
  • 12.4. Tests of Hypothesis in Factor Models
  • 12.5. Time Series
  • Exercises
  • References
  • 13. Bibliography of Related Recent Publications
  • Appendix A. Tables for the Chi-Square Adjustment Factor
  • Appendix B. Publications of the Author
  • Author Index
  • Subject Index
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