Normal view

## Applied multivariate statistical analysis / Richard A. Johnson, Dean W. Wichern.

Editor: Upper Saddle River, N.J. : Prentice Hall, c2007Edición: 6th edDescripción: xviii, 773 p. : il. ; 24 cmISBN: 0131877151Tema(s): Multivariate analysisOtra clasificación: 62-01 (62H15 62H25 62H30) Recursos en línea: Página web del libro
Contenidos:
```1 ASPECTS OF MULTIVARIATE ANALYSIS 
1.1 Introduction 
1.2 Applications of Multivariate Techniques 
1.3 The Organization of Data 
Arrays, 
Descriptive Statistics, 
Graphical Techniques, 
1.4 Data Displays and Pictorial Representations 
Linking Multiple Two-Dimensional Scatter Plots, 
Graphs of Growth Curves, 
Stars, 
Chernoff Faces, 
1.5 Distance 
Exercises 
References 
2 MATRIX ALGEBRA AND RANDOM VECTORS 
2.1 Introduction 
2.2 Some Basics of Matrix and Vector Algebra 
Vectors, 
Matrices, 
2.3 Positive Definite Matrices 
2.4 A Square-Root Matrix 
2.5 Random Vectors and Matrices 
2.6 Mean Vectors and Covariance Matrices 
Partitioning the Covariance Matrix, 
The Mean Vector and Covariance Matrix for Linear Combinations of Random Variables, 
Partitioning the Sample Mean Vector and Covariance Matrix, 
2.7 Matrix Inequalities and Maximization 
Supplement 2A: Vectors and Matrices: Basic Concepts 
Vectors, 
Matrices, 
Exercises 
References 
3 SAMPLE GEOMETRY AND RANDOM SAMPLING 
3.1 Introduction 
3.2 The Geometry of the Sample 
3.3 Random Samples and the Expected Values of the Sample Mean and Covariance Matrix 
3.4 Generalized Variance 
Situations in which the Generalized Sample Variance Is Zero, 
Generalized Variance Determined by | R | and Its Geometrical Interpretation, 
Another Generalization of Variance, 
3.5 Sample Mean, Covariance, and Correlation As Matrix Operations 
3.6 Sample Values of Linear Combinations of Variables 
Exercises 
References 
4 THE MULTIVARIATE NORMAL DISTRIBUTION 
4.1 Introduction 
4.2 The Multivariate Normal Density and Its Properties 
Additional Properties of the Multivariate Normal Distribution, 
4.3 Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation 
The Multivariate Normal Likelihood, 
Maximum Likelihood Estimation of μ and ∑, 
Sufficient Statistics, 
4.4 The Sampling Distribution of X and S 
Properties of the Wishart Distribution, 
4.5 Large-Sample Behavior of X and S 
4.6 Assessing the Assumption of Normality 
Evaluating the Normality of the Univariate Marginal Distributions, 
Evaluating Bivariate Normality, 
4.7 Detecting Outliers and Cleaning Data 
Steps for Detecting Outliers, 
4.8 Transformations to Near Normality 
Transforming Multivariate Observations, 
Exercises 
References 
5 INFERENCES ABOUT A MEAN VECTOR 
5.1 Introduction 
5.2 The Plausibility of μ0 Value for a Normal Population Mean 
5.3 Hotelling’s T2 and Likelihood Ratio Tests 
General Likelihood Ratio Method, 
5.4 Confidence Regions and Simultaneous Comparisons of Component Means 
Simultaneous Confidence Statements, 
A Comparison of Simultaneous Confidence Intervals with One-at-a-Time Intervals, 
The Bonferroni Method of Multiple Comparisons, 
5.5 Large Sample Inferences about a Population Mean Vector 
5.6 Multivariate Quality Control Charts 
Charts for Monitoring a Sample of Individual Multivariate Observations for Stability, 
Control Regions for Future Individual Observations, 
Control Ellipse for Future Observations, 
T2-Chart for Future Observations, 
Control Charts Based on Subsample Means, 
Control Regions for Future Subsample Observations, 
5.7 Inferences about Mean Vectors when Some Observations Are Missing 
5.8 Difficulties Due to Time Dependence in Multivariate Observations 
Supplement 5A: Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids 
Exercises 
References 
6 COMPARISONS OF SEVERAL MULTIVARIATE MEANS 
6.1 Introduction 
6.2 Paired Comparisons and a Repeated Measures Design 
Paired Comparisons, 
A Repeated Measures Design for Comparing Treatments, 
6.3 Comparing Mean Vectors from Two Populations 
Assumptions Concerning the Structure of the Data, 
Further Assumptions When n2 and n2 Are Small, 
Simultaneous Confidence Intervals, 
The Two-Sample Situation When ∑1 ≠ ∑2, 
An Approximation to the Distribution of T2 for Normal Populations When Sample Sizes Are Not Large, 
6.4 Comparing Several Multivariate Population Means (One-Way Manova) 
Assumptions about the Structure of the Data for One-Way MANOVA, 
A Summary of Univariate A NOVA, 
Multivariate Analysis of Variance (MANOVA), 
6.5 Simultaneous Confidence Intervals for Treatment Effects 
6.6 Testing for Equality of Covariance Matrices 
6.7 Two-Way Multivariate Analysis of Variance 
Univariate Two-Way Fixed-Effects Model with Interaction, 
Multivariate Two-Way Fixed-Effects Model with Interaction, 
6.8 Profile Analysis 
6.9 Repeated Measures Designs and Growth Curves 
6.10 Perspectives and a Strategy for Analyzing
Multivariate Models 
Exercises 
References 
7 MULTIVARIATE LINEAR REGRESSION MODELS 
7.1 Introduction 
7.2 The Classical Linear Regression Model 
7.3 Least Squares Estimation 
Sum-of-Squares Decomposition, 
Geometry of Least Squares, 
Sampling Properties of Classical Least Squares Estimators, 
7.4 Inferences About the Regression Model 
Inferences Concerning the Regression Parameters, 
Likelihood Ratio Tests for the Regression Parameters, 
7.5 Inferences from the Estimated Regression Function 
Estimating the Regression Function at z0, 
Forecasting a New Observation at z0, 
7.6 Model Checking and Other Aspects of Regression 
Does the Model Fit?, 
Leverage and Influence, 
Additional Problems in Linear Regression, 
T.T Multivariate Multiple Regression 
Likelihood Ratio Tests for Regression Parameters, 
Other Multivariate Test Statistics, 
Predictions from Multivariate Multiple Regressions, 
7.8 The Concept of Linear Regression 
Prediction of Several Variables, 
Partial Correlation Coefficient, 
7.9 Comparing the Two Formulations of the Regression Model 
Mean Corrected Form of the Regression Model, 
Relating the Formulations, 
7.10 Multiple Regression Models with Time Dependent Errors 
Supplement 7A: The Distribution of the Likelihood Ratio for the Multivariate Multiple Regression Model 
Exercises 
References  ```
```8 PRINCIPAL COMPONENTS 
8.1 Introduction 
8.2 Population Principal Components 
Principal Components Obtained from Standardized Variables, 
Principal Components for Covariance Matrices with Special Structures, 
8.3 Summarizing Sample Variation by Principal Components 
The Number of Principal Components, 
Interpretation of the Sample Principal Components, 
Standardizing the Sample Principal Components, 
8.4 Graphing the Principal Components 
8.5 Large Sample Inferences 
Large Sample Properties of λi and ei, 
Testing for the Equal Correlation Structure, 
8.6 Monitoring Quality with Principal Components 
Checking a Given Set of Measurements for Stability, 
Controlling Future Values, 
Supplement 8A: The Geometry of the Sample Principal Component Approximation 
The p-Dimensional Geometrical Interpretation, 
The n-Dimensional Geometrical Interpretation, 
Exercises 
References 
9 FACTOR ANALYSIS AND INFERENCE FOR STRUCTURED COVARIANCE MATRICES 
9.1 Introduction 
9.2 The Orthogonal Factor Model 
9.3 Methods of Estimation 
The Principal Component (and Principal Factor) Method, 
A Modified Approach—the Principal Factor Solution, 
The Maximum Likelihood Method, 
A Large Sample Test for the Number of Common Factors, 
9.4 Factor Rotation 
Oblique Rotations, 
9.5 Factor Scores 
The Weighted Least Squares Method, 
The Regression Method, 
9.6 Perspectives and a Strategy for Factor Analysis 
Supplement 9A: Some Computational Details for Maximum Likelihood Estimation 
Recommended Computational Scheme, 
Maximum Likelihood Estimators of p = LZLz' + ψz 
Exercises 
References 
10 CANONICAL CORRELATION ANALYSIS 
10.1 Introduction 
10.2 Canonical Variates and Canonical Correlations 
10.3 Interpreting the Population Canonical Variables 
Identifying the Canonical Variables, 
Canonical Correlations as Generalizations of Other Correlation Coefficients, 
The First r Canonical Variables as a Summary of Variability, 
A Geometrical Interpretation of the Population Canonical Correlation Analysis 
10.4 The Sample Canonical Variates and Sample
Canonical Correlations 
10.5 Additional Sample Descriptive Measures 558 Matrices of Errors of Approximations, 558 Proportions of Explained Sample Variance, 
10.6 Large Sample Inferences 
Exercises 
References 
11 DISCRIMINATION AND CLASSIFICATION 
11.1 Introduction 
11.2 Separation and Classification for Two Populations 
11.3 Classification with Two Multivariate Normal Populations 
Classification of Normal Populations When ∑1 = ∑2 = ∑, 584 Scaling, 
Fisher’s Approach to Classification with Two Populations, 
Is Classification a Good Idea?, 
Classification of Normal Populations When ∑1 ≠ ∑2 ,593
11.4 Evaluating Classification Functions 
11.5 Classification with Several Populations 
The Minimum Expected Cost of Misclassification Method, 606 Classification with Normal Populations, 
11.6 Fisher’s Method for Discriminating among Several Populations 
Using Fisher’s Discriminants to Classify Objects, 
11.7 Logistic Regression and Classification 
Introduction, 
The Logit Model, 
Logistic Regression Analysis, 
Classification, 
Logistic Regression with Binomial Responses, 
Including Qualitative Variables, 
Classification Trees, 
Neural Networks, 
Selection of Variables, 
Testing for Group Differences, 
Graphics, 
Practical Considerations Regarding Multivariate Normality, 
Exercises 
References 
12 CLUSTERING, DISTANCE METHODS, AND ORDINATION 
12.1 Introduction 
12.2 Similarity Measures 
Distances and Similarity Coefficients for Pairs of Items, 
Similarities and Association Measures for Pairs of Variables, 
12.3 Hierarchical Clustering Methods 
Ward’s Hierarchical Clustering Method, 
12.4 Nonhierarchical Clustering Methods 
K-means Method, 
12.5 Clustering Based on Statistical Models 
12.6 Multidimensional Scaling 
The Basic Algorithm, 
12.7 Correspondence Analysis 
Algebraic Development of Correspondence Analysis, 718 Inertia, 
Interpretation in Two Dimensions, 
12.8 Biplots for Viewing Sampling Units and Variables 
Constructing Biplots, 
12.9 Procrustes Analysis: A Method
for Comparing Configurations 
Constructing the Procrustes Measure of Agreement, 
Supplement 12A: Data Mining 
Introduction, 
The Data Mining Process, 
Model Assessment, 
Exercises 
References 
APPENDIX 
DATA INDEX 
SUBJECT INDEX  --``` Average rating: 0.0 (0 votes)
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Incluye referencias bibliográficas (p. 755-756) e índices.

1 ASPECTS OF MULTIVARIATE ANALYSIS  --
1.1 Introduction  --
1.2 Applications of Multivariate Techniques  --
1.3 The Organization of Data  --
Arrays,  --
Descriptive Statistics,  --
Graphical Techniques,  --
1.4 Data Displays and Pictorial Representations  --
Linking Multiple Two-Dimensional Scatter Plots,  --
Graphs of Growth Curves,  --
Stars,  --
Chernoff Faces,  --
1.5 Distance  --
Exercises  --
References  --
2 MATRIX ALGEBRA AND RANDOM VECTORS  --
2.1 Introduction  --
2.2 Some Basics of Matrix and Vector Algebra  --
Vectors,  --
Matrices,  --
2.3 Positive Definite Matrices  --
2.4 A Square-Root Matrix  --
2.5 Random Vectors and Matrices  --
2.6 Mean Vectors and Covariance Matrices  --
Partitioning the Covariance Matrix,  --
The Mean Vector and Covariance Matrix for Linear Combinations of Random Variables,  --
Partitioning the Sample Mean Vector and Covariance Matrix,  --
2.7 Matrix Inequalities and Maximization  --
Supplement 2A: Vectors and Matrices: Basic Concepts  --
Vectors,  --
Matrices,  --
Exercises  --
References  --
3 SAMPLE GEOMETRY AND RANDOM SAMPLING  --
3.1 Introduction  --
3.2 The Geometry of the Sample  --
3.3 Random Samples and the Expected Values of the Sample Mean and Covariance Matrix  --
3.4 Generalized Variance  --
Situations in which the Generalized Sample Variance Is Zero,  --
Generalized Variance Determined by | R | and Its Geometrical Interpretation,  --
Another Generalization of Variance,  --
3.5 Sample Mean, Covariance, and Correlation As Matrix Operations  --
3.6 Sample Values of Linear Combinations of Variables  --
Exercises  --
References  --
4 THE MULTIVARIATE NORMAL DISTRIBUTION  --
4.1 Introduction  --
4.2 The Multivariate Normal Density and Its Properties  --
Additional Properties of the Multivariate Normal Distribution,  --
4.3 Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation  --
The Multivariate Normal Likelihood,  --
Maximum Likelihood Estimation of μ and ∑,  --
Sufficient Statistics,  --
4.4 The Sampling Distribution of X and S  --
Properties of the Wishart Distribution,  --
4.5 Large-Sample Behavior of X and S  --
4.6 Assessing the Assumption of Normality  --
Evaluating the Normality of the Univariate Marginal Distributions,  --
Evaluating Bivariate Normality,  --
4.7 Detecting Outliers and Cleaning Data  --
Steps for Detecting Outliers,  --
4.8 Transformations to Near Normality  --
Transforming Multivariate Observations,  --
Exercises  --
References  --
5 INFERENCES ABOUT A MEAN VECTOR  --
5.1 Introduction  --
5.2 The Plausibility of μ0 Value for a Normal Population Mean  --
5.3 Hotelling’s T2 and Likelihood Ratio Tests  --
General Likelihood Ratio Method,  --
5.4 Confidence Regions and Simultaneous Comparisons of Component Means  --
Simultaneous Confidence Statements,  --
A Comparison of Simultaneous Confidence Intervals with One-at-a-Time Intervals,  --
The Bonferroni Method of Multiple Comparisons,  --
5.5 Large Sample Inferences about a Population Mean Vector  --
5.6 Multivariate Quality Control Charts  --
Charts for Monitoring a Sample of Individual Multivariate Observations for Stability,  --
Control Regions for Future Individual Observations,  --
Control Ellipse for Future Observations,  --
T2-Chart for Future Observations,  --
Control Charts Based on Subsample Means,  --
Control Regions for Future Subsample Observations,  --
5.7 Inferences about Mean Vectors when Some Observations Are Missing  --
5.8 Difficulties Due to Time Dependence in Multivariate Observations  --
Supplement 5A: Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids  --
Exercises  --
References  --
6 COMPARISONS OF SEVERAL MULTIVARIATE MEANS  --
6.1 Introduction  --
6.2 Paired Comparisons and a Repeated Measures Design  --
Paired Comparisons,  --
A Repeated Measures Design for Comparing Treatments,  --
6.3 Comparing Mean Vectors from Two Populations  --
Assumptions Concerning the Structure of the Data,  --
Further Assumptions When n2 and n2 Are Small,  --
Simultaneous Confidence Intervals,  --
The Two-Sample Situation When ∑1 ≠ ∑2,  --
An Approximation to the Distribution of T2 for Normal Populations When Sample Sizes Are Not Large,  --
6.4 Comparing Several Multivariate Population Means (One-Way Manova)  --
Assumptions about the Structure of the Data for One-Way MANOVA,  --
A Summary of Univariate A NOVA,  --
Multivariate Analysis of Variance (MANOVA),  --
6.5 Simultaneous Confidence Intervals for Treatment Effects  --
6.6 Testing for Equality of Covariance Matrices  --
6.7 Two-Way Multivariate Analysis of Variance  --
Univariate Two-Way Fixed-Effects Model with Interaction,  --
Multivariate Two-Way Fixed-Effects Model with Interaction,  --
6.8 Profile Analysis  --
6.9 Repeated Measures Designs and Growth Curves  --
6.10 Perspectives and a Strategy for Analyzing --
Multivariate Models  --
Exercises  --
References  --
7 MULTIVARIATE LINEAR REGRESSION MODELS  --
7.1 Introduction  --
7.2 The Classical Linear Regression Model  --
7.3 Least Squares Estimation  --
Sum-of-Squares Decomposition,  --
Geometry of Least Squares,  --
Sampling Properties of Classical Least Squares Estimators,  --
7.4 Inferences About the Regression Model  --
Inferences Concerning the Regression Parameters,  --
Likelihood Ratio Tests for the Regression Parameters,  --
7.5 Inferences from the Estimated Regression Function  --
Estimating the Regression Function at z0,  --
Forecasting a New Observation at z0,  --
7.6 Model Checking and Other Aspects of Regression  --
Does the Model Fit?,  --
Leverage and Influence,  --
Additional Problems in Linear Regression,  --
T.T Multivariate Multiple Regression  --
Likelihood Ratio Tests for Regression Parameters,  --
Other Multivariate Test Statistics,  --
Predictions from Multivariate Multiple Regressions,  --
7.8 The Concept of Linear Regression  --
Prediction of Several Variables,  --
Partial Correlation Coefficient,  --
7.9 Comparing the Two Formulations of the Regression Model  --
Mean Corrected Form of the Regression Model,  --
Relating the Formulations,  --
7.10 Multiple Regression Models with Time Dependent Errors  --
Supplement 7A: The Distribution of the Likelihood Ratio for the Multivariate Multiple Regression Model  --
Exercises  --
References  --

8 PRINCIPAL COMPONENTS  --
8.1 Introduction  --
8.2 Population Principal Components  --
Principal Components Obtained from Standardized Variables,  --
Principal Components for Covariance Matrices with Special Structures,  --
8.3 Summarizing Sample Variation by Principal Components  --
The Number of Principal Components,  --
Interpretation of the Sample Principal Components,  --
Standardizing the Sample Principal Components,  --
8.4 Graphing the Principal Components  --
8.5 Large Sample Inferences  --
Large Sample Properties of λi and ei,  --
Testing for the Equal Correlation Structure,  --
8.6 Monitoring Quality with Principal Components  --
Checking a Given Set of Measurements for Stability,  --
Controlling Future Values,  --
Supplement 8A: The Geometry of the Sample Principal Component Approximation  --
The p-Dimensional Geometrical Interpretation,  --
The n-Dimensional Geometrical Interpretation,  --
Exercises  --
References  --
9 FACTOR ANALYSIS AND INFERENCE FOR STRUCTURED COVARIANCE MATRICES  --
9.1 Introduction  --
9.2 The Orthogonal Factor Model  --
9.3 Methods of Estimation  --
The Principal Component (and Principal Factor) Method,  --
A Modified Approach—the Principal Factor Solution,  --
The Maximum Likelihood Method,  --
A Large Sample Test for the Number of Common Factors,  --
9.4 Factor Rotation  --
Oblique Rotations,  --
9.5 Factor Scores  --
The Weighted Least Squares Method,  --
The Regression Method,  --
9.6 Perspectives and a Strategy for Factor Analysis  --
Supplement 9A: Some Computational Details for Maximum Likelihood Estimation  --
Recommended Computational Scheme,  --
Maximum Likelihood Estimators of p = LZLz' + ψz  --
Exercises  --
References  --
10 CANONICAL CORRELATION ANALYSIS  --
10.1 Introduction  --
10.2 Canonical Variates and Canonical Correlations  --
10.3 Interpreting the Population Canonical Variables  --
Identifying the Canonical Variables,  --
Canonical Correlations as Generalizations of Other Correlation Coefficients,  --
The First r Canonical Variables as a Summary of Variability,  --
A Geometrical Interpretation of the Population Canonical Correlation Analysis  --
10.4 The Sample Canonical Variates and Sample --
Canonical Correlations  --
10.5 Additional Sample Descriptive Measures 558 Matrices of Errors of Approximations, 558 Proportions of Explained Sample Variance,  --
10.6 Large Sample Inferences  --
Exercises  --
References  --
11 DISCRIMINATION AND CLASSIFICATION  --
11.1 Introduction  --
11.2 Separation and Classification for Two Populations  --
11.3 Classification with Two Multivariate Normal Populations  --
Classification of Normal Populations When ∑1 = ∑2 = ∑, 584 Scaling,  --
Fisher’s Approach to Classification with Two Populations,  --
Is Classification a Good Idea?,  --
Classification of Normal Populations When ∑1 ≠ ∑2 ,593 --
11.4 Evaluating Classification Functions  --
11.5 Classification with Several Populations  --
The Minimum Expected Cost of Misclassification Method, 606 Classification with Normal Populations,  --
11.6 Fisher’s Method for Discriminating among Several Populations  --
Using Fisher’s Discriminants to Classify Objects,  --
11.7 Logistic Regression and Classification  --
Introduction,  --
The Logit Model,  --
Logistic Regression Analysis,  --
Classification,  --
Logistic Regression with Binomial Responses,  --
Including Qualitative Variables,  --
Classification Trees,  --
Neural Networks,  --
Selection of Variables,  --
Testing for Group Differences,  --
Graphics,  --
Practical Considerations Regarding Multivariate Normality,  --
Exercises  --
References  --
12 CLUSTERING, DISTANCE METHODS, AND ORDINATION  --
12.1 Introduction  --
12.2 Similarity Measures  --
Distances and Similarity Coefficients for Pairs of Items,  --
Similarities and Association Measures for Pairs of Variables,  --
Concluding Comments on Similarity,  --
12.3 Hierarchical Clustering Methods  --
Ward’s Hierarchical Clustering Method,  --
12.4 Nonhierarchical Clustering Methods  --
K-means Method,  --
12.5 Clustering Based on Statistical Models  --
12.6 Multidimensional Scaling  --
The Basic Algorithm,  --
12.7 Correspondence Analysis  --
Algebraic Development of Correspondence Analysis, 718 Inertia,  --
Interpretation in Two Dimensions,  --
12.8 Biplots for Viewing Sampling Units and Variables  --
Constructing Biplots,  --
12.9 Procrustes Analysis: A Method --
for Comparing Configurations  --
Constructing the Procrustes Measure of Agreement,  --
Supplement 12A: Data Mining  --
Introduction,  --
The Data Mining Process,  --
Model Assessment,  --
Exercises  --
References  --
APPENDIX  --
DATA INDEX  --
SUBJECT INDEX  --

MR, 2009d:62001

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