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Applied Multivariate Data Analysis : Volume II: Categorical and Multivariate Methods

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概要 A Second Course in Statistics The past decade has seen a tremendous increase in the use of statistical data analysis and in the availability of both computers and statistical software. Business and go...vernment professionals, as well as academic researchers, are now regularly employing techniques that go far beyond the standard two-semester, introductory course in statistics. Even though for this group of users shorl courses in various specialized topics are often available, there is a need to improve the statistics training of future users of statistics while they are still at colleges and universities. In addition, there is a need for a survey reference text for the many practitioners who cannot obtain specialized courses. With the exception of the statistics major, most university students do not have sufficient time in their programs to enroll in a variety of specialized one-semester courses, such as data analysis, linear models, experimental de sign, multivariate methods, contingency tables, logistic regression, and so on. There is a need for a second survey course that covers a wide variety of these techniques in an integrated fashion. It is also important that this sec ond course combine an overview of theory with an opportunity to practice, including the use of statistical software and the interpretation of results obtained from real däta.続きを見る
目次 6 Contingency Tables
6.1 Multivariate Data Analysis Data Matrices and Measurement Scales
6.2 Two-Dimensional Contingency Tables
6.3 Multidimensional Contingency Tables
6.4 The Weighted Least Squares Approach
Cited Literature and References
Exercises for Chapter 6
Questions for Chapter 6
7 Multivariate Distributions Inference Regression and Canonical Correlation
7.1 Multivariate Random Variables and Samples
7.2 The Multivariate Normal Distribution
7.3 Testing for Normality Outliers and Robust Estimation
7.4 Inference for the Multivariate Normal
7.5 Multivariate Regression and Canonical Correlation
Cited Literature and References
Exercises for Chapter 7
Questions for Chapter 7
8 Manova Discriminant Analysis and Qualitative Response Models
8.1 Multivariate Analysis of Variance
8.2 Discriminant Analysis
8.3 Qualitative Response Regression Models and Logistic Regression
9 Principal Components Factors and Correspondence Analysis
9.1 Principal Components
9.2 The Exploratory Factor Analysis Model
9.3 Singular Value Decomposition and Matrix Approximation
9.4 Correspondence Analysis
Cited Literature and References
Exercises for Chapter 9
Questions for Chapter 9
10 Cluster Analysis and Multidimensional Scaling
10.1 Proximity Matrices Derived from Data Matrices
10.2 Cluster Analysis
10.3 Multidimensional Scaling
Cited Literature and References
Exercises for Chapter 10
Questions for Chapter 10
1. Matrix Algebra
1.1 Matrices
Matrix
Transpose of a Matrix
Row Vector and Column Vector
Square Matrix
Symmetric Matrix
Diagonal Elements
Trace of a Matrix
Null or Zero Matrix
Identity Matrix
Diagonal Matrix
Submatrix
1.2 Matrix Operations
Equality of Matrices
Addition of Matrices
Additive Inverse
Scalar Multiplication of a Matrix
Product of Two Matrices
Multiplicative Inverse
Idempotent Matrix
Kronecker Product
1.3 Determinants and Rank
Determinant
Nonsingular
Relation Between Inverse
and Determinant
Rank of a Matrix
1.4 Quadratic Forms and Positive Definite Matrices
Quadratic Form
Congruent Matrix
Positive Definite
Positive Semidefinite
Negative Definite
Non-negative Definite
1.5 Partitioned Matrices
Product of Partitioned Matrices
Inverse of a Parti-tioned Matrix
Determinant of a Partitioned Matrix
1.6 Expectations of Random Matrices
1.7 Derivatives of Matrix Expressions
2. Linear Algebra
2.1 Geometric Representation for Vectors
n Dimensional Space
Directed Line Segment
Coordinates
Addition of Vectors
Scalar Multiplication
Length of a Vector
Angle Between Vectors
Orthogonal Vectors
Projection
2.2 Linear Dependence And Linear Transformations
Linearly Dependent Vectors
Linearly Independent Vectors
Basis for an n-Dimensional Space
Generation of a Vector Space and Rank of a Matrix
Linear Transformation
Orthogonal Transformation
Rotation
Orthogonal Matri
2.3 Systems of Equations
Solution Vector for a System of Equations
Homoge-neous Equations - Trivial and Nontrivial Solutions
2.4 Column Spaces
Projection Operators and Least
Squares
Column Space
Orthogonal Complement
Projection
Ordinary Least Squares Solution Vector
Idempotent Matrix - Projection Operator
3. Eigenvalue Structure and Singular Value Decomposition
3.1 Eigenvalue Structure for Square Matrices
Eigenvalues and Eigenvectors
Characteristic Polynomial
Characteristic Roots
Latent Roots
Eigen-values
Eigenvalues and Eignevectors for Real Symmetric Matrices and Some Properties
Spectral Decomposition
Matrix Approximation
Eigenvalues for Nonnegative Definite Matrices
3.2 Singular Value Decomposition
Left and Right Singular Vectors
Complete Singular Value Decomposition
Generalized Singular Value Decomposition
Relationship to Spectral Decomposition and Eigenvalues
Data Appendix For Volume II
Data Set V1
Data Set V2
Data Set V3
Data Set V4
Data Set V5
Data Set V6
Data Set V7
Data Set V8
Data Set V9
Data Set V10
Data Set Vll
Data Set V12
Data Set V13
Data Set V14
Data Set V15
Data Set V16
Data Set V17
Data Set V18
Data Set V19
Data Set V20
Data Set V21
Data Set V22
Table V1
Table V2
Table V3
Table V4
Table V5
Table V6
Table V7
Table V8
Table V9
Table V10
Table V11
Table V12
Table V13
Table V14
Table V15
Table V16
Table V17
Table V18
Table V19
Table V20
Table V21
Table V22
Author Index.
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登録日 2020.06.27
更新日 2020.06.28