Applied Multivariate Statistical Analysis

by Johnson, Richard A.; Wichern, Dean W.

• ISBN13: 9780131877153
• ISBN10: 0131877151
• Edition: 6th
• Format: Hardcover
• Copyright: 2007-03-23
• Publisher: Pearson

Summary

This market leader offers a readable introduction to the statistical analysis of multivariate observations. Gives readers the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. Starts with a formulation of the population models, delineates the corresponding sample results, and liberally illustrates everything with examples. Offers an abundance of examples and exercises based on real data. Appropriate for experimental scientists in a variety of disciplines.

Author Biography

Dean W. Wichern is Professor Emeritus at the Mays School of Business at Texas A&M University. He holds membership in the American Statistical Association, Royal Statistical Society, International Institute of Forecasters, and Institute for Operations Research and the Management Sciences. He is the author for four textbooks and was Associate Editor of  Journal of Business and Economic Statistics from 1983-1991.

 

                  

Professor Richard A. Johnson is Professor in the Department of Statistics at the University of Wisconsin. He is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association and he is amember of the Royal Statistical Society and International Statistical Institute. He is the author of six textbooks and over 120 technical publications and is the founding Editor of Statistics and Probability Letters (1981-).

Table of Contents

DRAFT (NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.)

Getting Started

Aspects of Multivariate Analysis

Applications of Multivariate Techniques

The Organization of Data

Data Displays and Pictorial Representations

Distance

Final Comments

Matrix Algebra and Random Vectors

Some Basics of Matrix and Vector Algebra

Positive Definite Matrices

A Square-Root Matrix

Random Vectors and Matrices

Mean Vectors and Covariance Matrices

Matrix Inequalities and Maximization

Supplement 2A Vectors and Matrices: Basic Concepts

Sample Geometry and Random Sampling

The Geometry of the Sample

Random Samples and the Expected Values of the Sample Mean and Covariance Matrix

Generalized Variance

Sample Mean, Covariance, and Correlation as Matrix Operations

Sample Values of Linear Combinations of Variables

The Multivariate Normal Distribution

The Multivariate Normal Density and Its Properties

Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation

The Sampling Distribution of `X and S. Large-Sample Behavior of `X and S. Assessing the Assumption of Normality

Detecting Outliners and Data Cleaning

Transformations to Near Normality

Inferences About Multivariate Means and Linear Models

Inferences About a Mean Vector

The Plausibility of m0 as a Value for a Normal Population Mean

Hotelling's T 2 and Likelihood Ratio Tests

Confidence Regions and Simultaneous Comparisons of Component Means

Large Sample Inferences about a Population Mean Vector

Multivariate Quality Control Charts

Inferences about Mean Vectors When Some Observations Are Missing

Difficulties Due To Time Dependence in Multivariate Observations

Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids

Comparisons of Several Multivariate Means

Paired Comparisons and a Repeated Measures Design

Comparing Mean Vectors from Two Populations

Comparison of Several Multivariate Population Means (One-Way MANOVA). Simultaneous Confidence Intervals for Treatment Effects

Two-Way Multivariate Analysis of Variance

Profile Analysis

Repealed Measures, Designs, and Growth Curves

Perspectives and a Strategy for Analyzing Multivariate Models

Multivariate Linear Regression Models

The Classical Linear Regression Model

Least Squares Estimation

Inferences About the Regression Model

Inferences from the Estimated Regression Function

Model Checking and Other Aspects of Regression

Multivariate Multiple Regression

The Concept of Linear Regression

Comparing the Two Formulations of the Regression Model

Multiple Regression Models with Time Dependant Errors

Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model

Analysis Of A Covariance Structure

Principal Components

Population Principal Components

Summarizing Sample Variation by Principal Components

Graphing the Principal Components

Large-Sample Inferences

Monitoring Quality with Principal Components

Supplement 8A The Geometry of the Sample Principal Component Approximation

Factor Analysis and Inference for Structured Covariance Matrices

The Orthogonal Factor Model

Methods of Estimation

Factor Rotation

Factor Scores

Perspectives and a Strategy for Factor Analysis

Structural Equation Models

Supplement 9A Some Computational Details for Maximum Likelihood Estimation

Canonical Correlation Analysis

Canonical Variates and Canonical Correlations

Interpreting the Population Canonical Variables

The Sample Canonical Variates and Sample Canonical Correlations

Additional Sample Descriptive Meas

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