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A First Course in Multivariate Statistics

  • Fester Einband
  • 736 Seiten
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This is author-approved bcc: Multivariate statistical methods have evolved from the pioneering work of Fisher, Pearson, Hotelling,... Weiterlesen
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Beschreibung

This is author-approved bcc: Multivariate statistical methods have evolved from the pioneering work of Fisher, Pearson, Hotelling,and others, motivated by practical problems in biological and other sciences. In the past fifty years the field has grown rapidly, largely due to the availability of computers that make the calculations feasible. This book gives a comprehensive and self-contained introduction, carefully balancing mathematical theory and practical applications. "A First Course in Multivariate Statistics" starts at an elementary level, developing concepts of multivariate distributions from first principles. A chapter on the multivariate normal distribution reviews the classical parametric theory. Methods of estimation are explored using the plug-in principles as well as maximum likelihood. Two chapters on discrimination and classification, including logistic regression, are at the core of the book. Methods of testing hypotheses are developed from heuristic principles, followed by likelihood ratio tests and permutation tests. The powerful self- consistency principle is used to introduce principal components as a method of approximation. The book concludes with a chapter on finite mixture analysis, a topic of great practical and theoretical importance. Unique features of "A First Course in Multivariate Statistics" include the presentation of the EM algorithm for maximum likelihood estimation with incomplete data, resampling based methods of testing, a brief introduction to the theory of elliptical distributions, and a comparison of linear and quadratic classification rules. Examples from biology, anthropology, chemistry, and other area are worked out.

Zusammenfassung
Two chapters on discrimination and classification, including logistic regression, form the core of the book, followed by methods of testing hypotheses developed from heuristic principles, likelihood ratio tests and permutation tests.

Inhalt

1. Why Multivariate Statistics?.- 2. Joint Distribution of Several Random Variables.- 3. The Multivariate Normal Distribution.- 4. Parameter Estimation.- 5. Discrimination and Classification, Round 1.- 6. Statistical Inference for Means.- 7. Discrimination and Classification, Round 2.- 8. Linear Principal Component Analysis.- 9. Normal Mixtures.- Appendix: Selected Results From Matrix Algebra.- A.0. Preliminaries.- A.1. Partitioned Matrices.- A.2. Positive Definite Matrices.- A.3. The Cholesky Decomposition.- A.4. Vector and Matrix Differentiation.- A.5. Eigenvectors and Eigenvalues.- A.6. Spectral Decomposition of Symmetric Matrices.- A.7. The Square Root of a Positive Definite Symmetric Matrix.- A.8. Orthogonal Projections on Lines and Planes.- A.9. Simultaneous Decomposition of Two Symmetric Matrices.

Produktinformationen

Titel: A First Course in Multivariate Statistics
Autor:
EAN: 9780387982069
ISBN: 038798206X
Format: Fester Einband
Herausgeber: Springer New York
Genre: Mathematik
Anzahl Seiten: 736
Gewicht: 1608g
Größe: H248mm x B198mm x T44mm
Jahr: 1997
Auflage: 1997

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