Methods of multivariate analysis /

"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 reader...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Rencher, Alvin C., 1934-
Otros Autores: Christensen, William F., 1970-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Hoboken, New Jersey : Wiley, 2012.
Edición:Third edition.
Colección:Wiley series in probability and statistics
Temas:
Multivariate analysis.
Multivariate Analysis
MATHEMATICS > Probability & Statistics > Multivariate Analysis.
Multivariate analysis > Data processing.
Multivariate analysis > Graphic methods.
Analyse multivariée.
Multivariate analysis
Anàlisi multivariable.
Llibres electrònics.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 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
  • 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.
  • 5.4. COMPARING TWO MEAN VECTORS.

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