Multivariate Analysis. Kendall's Library of Statistics, Volume 1 Part 1

  • ID: 2171105
  • Book
  • 292 Pages
  • John Wiley and Sons Ltd
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A common and important statistical technique, multivariate analysis has applications in a wide range of fields of study including subjects as diverse as biology and linguistics. This two part overview provides comprehensive coverage of all the available techniques for analyzing data in this form. The first part, on distributions, ordination and inference, concentrates on basic techniques. While full technical details are supplied, the emphasis throughout is on a readable and user–friendly presentation with ample use of illustrative exercises.
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Preface.

1 Introduction.

Multivariate data.

Populations and samples.

Multivariate description.

Models and inference.

Computer–intensive methods.

Missing values.

Scope of this book.

2 Multivariate Distributions.

Distribution theory.

Marginal and conditional distributions.

Transformations.

Second order analysis.

The multivariate normal distribution.

Spherical and elliptical distributions.

The Dirichlet distribution.

Distributions for compositional data.

Generalisations of the Gamma distribution.

Multivariate discrete distributions.

The multinomial distribution.

The multivariate hypergeometric distribution.

The multivariate Poisson distribution.

Mixed binary and continuous data.

Multivariate stable distributions.

Matrix–valued distributions.

Exercises.

3 Initial Data Analysis.

Graphical displays of multivariate data.

The detection of outliners.

Tests of normality.

Transformations of data.

Descriptive statistics for multivariate data.

Similarity, dissimilarity and distance.

Exercises.

4 Projections and Linear Transformations.

Principal components.

Scaling.

Size and shape.

Population principal components.

Choosing subsets of variables.

Three–mode component analysis.

Comparison with other techniques.

Biplots.

Canonical variables.

Canonical variables in classification.

Projection pursuit.

Criteria for projection pursuit.

Projection pursuit and significance testing.

Projection pursuit regression.

Projection pursuit density estimation.

Function optimization.

Exercises.

5 Distance Methods and Ordination.

Ordination.

Proximity matrices.

Geometrical objectives and fundamentals.

Metric scaling.

Non–metric scaling.

Individual differences.

Contingency tables.

Correspondence analysis.

Indicator matrices and higher–order tables.

Procrustes analysis.

Generalised Procrustes analysis.

Exercises.

6 Inference: Estimation and Hypothesis Testing.

Point estimation.

Interval and region estimation.

Hypothesis testing.

Single–sample normal data: tests of the mean.

Single–sample normal data: tests of dispersion.

Multi–sample normal data.

Non–normality.

Exercises.

7 Multivariate Linear Models.

The univariate linear model.

The multivariate linear model.

Multivariate calibration.

Inference in the multivariate linear model.

Multivariate analysis of variance.

Multivariate analysis of covariance.

Simultaneous inference.

Presentation of means.

Selection of variables.

Redundancy indices and redundancy analysis.

Exercise.

8 Nonlinear Methods.

Nonlinear principal components.

Nonlinear biplots.

General nonlinear systems.

The Gifi system.

Distance approach.

Exercises.

A Appendix A. Normal Theory Sampling Distributions.

Multivariate generalization of Student s t.

Further properties of the Mahalanobis distance.

The Wishart distribution.

Related distributions.

Likelihood ratio tests.

Union–intersection tests.

Testing linear models.

Choice of test statistic.

A test of dimensionality.

Eigenvalue distributions.

References.

Author Index.

Subject Index.
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W. J. Krzanowski
F. H. C. Marriott
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