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Bilinear Forms and Zonal Polynomials - Arak M. Mathai|Serge B. Provost|Takesi Hayakawa
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Bilinear Forms and Zonal Polynomials - Taschenbuch

1995, ISBN: 0387945229

[EAN: 9780387945224], Neubuch, [PU: Springer New York], LIKELIHOOD NORMALDISTRIBUTION BINOMIAL CORRELATION STATISTICS MATHEMATIK WAHRSCHEINLICHKEITSTHEORIE STOCHASTIK MATHEMATISCHE STATIS… Mehr…

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*Bilinear Forms and Zonal Polynomials* - Softcover reprint of the original 1st ed. 1995 / Taschenbuch für 53.49 € / Aus dem Bereich: Bücher, Wissenschaft, Mathematik Medien > Bücher nein … Mehr…

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Bilinear Forms and Zonal Polynomials (Lecture Notes in Statistics, 102) - Mathai, Arak M.; Provost, Serge B.; Hayakawa, Takesi
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Mathai, Arak M.; Provost, Serge B.; Hayakawa, Takesi:
Bilinear Forms and Zonal Polynomials (Lecture Notes in Statistics, 102) - Taschenbuch

1995

ISBN: 0387945229

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Arak M. Mathai; Serge B. Provost; Takesi Hayakawa:
Bilinear Forms and Zonal Polynomials - Taschenbuch

1995, ISBN: 9780387945224

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Bilinear Forms and Zonal Polynomials (Lecture Notes in Statistics, 102) - Mathai, Arak M.; Provost, Serge B.; Hayakawa, Takesi
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Mathai, Arak M.; Provost, Serge B.; Hayakawa, Takesi:
Bilinear Forms and Zonal Polynomials (Lecture Notes in Statistics, 102) - Taschenbuch

1995, ISBN: 0387945229

[EAN: 9780387945224], Neubuch, [PU: Springer], Book is in NEW condition., Books

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Details zum Buch
Bilinear Forms and Zonal Polynomials

This monograph deals with bilinear forms in real random vectors and their generalizations. The authors show how zonal polynomials may be used to analyze such forms and thus to apply these concepts in a variety of statistical settings. Assuming a graduate-level background in statistics, this account is self-contained and each chapter concludes with exercises making the book ideal for a researcher seeking a straight-forward introduction to this topic. Chapter 1 covers preliminaries including a treatment of the Jacobians of matrix transformation and chapter 2 then introduces bilinear forms in Gaussian random real vectors. Chapter 3 covers quadratic forms in elliptically contoured and spherically symmetric vectors whilst chapters 4 and 5 introduce and then apply the theory of zonal polynomials to the theory of distributions of generalized quadratic and bilinear forms.

Detailangaben zum Buch - Bilinear Forms and Zonal Polynomials


EAN (ISBN-13): 9780387945224
ISBN (ISBN-10): 0387945229
Taschenbuch
Erscheinungsjahr: 1995
Herausgeber: Springer New York
392 Seiten
Gewicht: 0,591 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-11-08T12:09:27+01:00 (Berlin)
Detailseite zuletzt geändert am 2024-01-10T10:51:25+01:00 (Berlin)
ISBN/EAN: 0387945229

ISBN - alternative Schreibweisen:
0-387-94522-9, 978-0-387-94522-4
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: hayakawa, provost, provo, serge, arak mathai
Titel des Buches: polynomials, zona


Daten vom Verlag:

Autor/in: Arak M. Mathai; Serge B. Provost; Takesi Hayakawa
Titel: Lecture Notes in Statistics; Bilinear Forms and Zonal Polynomials
Verlag: Springer; Springer US
376 Seiten
Erscheinungsjahr: 1995-05-19
New York; NY; US
Sprache: Englisch
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
Available
XII, 376 p.

BC; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Wahrscheinlichkeitsrechnung und Statistik; Verstehen; Likelihood; Normal distribution; binomial; correlation; statistics; Probability Theory; Stochastik; EA

1 Preliminaries.- 1.0 Introduction.- 1.1 Jacobians of Matrix Transformations.- 1.1a Some Frequently Used Jacobians in the Real Case.- 1.2 Singular and Nonsingular Normal Distributions.- 1.2a Normal Distribution in the Real Case.- 1.2b The Moment Generating Function for the Real Normal Distribution.- 1.3 Quadratic Forms in Normal Variables.- 1.3a Representations of a Quadratic Form.- 1.3b Representations of the m. g. f. of a Quadratic Expression.- 1.4 Matrix-variate Gamma and Beta Functions.- 1.4a Matrix-variate Gamma, Real Case.- 1.4b Matrix-variate Gamma Density, Real Case.- 1.4c The m. g. f. of a Matrix-variate Real Gamma Variable.- 1.4d Matrix-variate Beta, Real Case.- 1.5 Hypergeometric Series, Real Case.- 2 Quadratic and Bilinear Forms in Normal Vectors.- 2.0 Introduction.- 2.1 Various Representations.- 2.2 Density of a Gamma Difference.- 2.2a Some Particular Cases.- 2.3 Noncentral Gamma Difference.- 2.4 Moments and Cumulants of Bilinear Forms.- 2.4a Joint Moments and Cumulants of Quadratic and Bilinear Forms.- 2.4b Joint Cumulants of Bilinear Forms.- 2.4c Moments and Cumulants in the Singular Normal Case.- 2.4d Cumulants of Bilinear Expressions.- 2.5 Laplacianness of Bilinear Forms.- 2.5a Quadratic and Bilinear Forms in the Nonsingular Normal Case.- 2.5b NS Conditions for the Noncorrelated Normal Case.- 2.5c Quadratic and Bilinear Forms in the Singular Normal Case.- 2.5d Noncorrelated Singular Normal Case.- 2.5e The NS Conditions for a Quadratic Form to be NGL.- 2.6 Generalizations to Bilinear and Quadratic Expressions.- 2.6a Bilinear and Quadratic Expressions in the Nonsingular Normal Case.- 2.6b Bilinear and Quadratic Expressions in the Singular Normal Case.- 2.7 Independence of Bilinear and Quadratic Expressions.- 2.7a Independence of a Bilinear and a QuadraticForm.- 2.7b Independence of Two Bilinear Forms.- 2.7c Independence of Quadratic Expressions: Nonsingular Normal Case.- 2.7d Independence in the Singular Normal Case.- 2.8 Bilinear Forms and Noncentral Gamma Differences.- 2.8a Bilinear Forms in the Equicorrelated Case.- 2.8b Noncentral Case.- 2.9 Rectangular Matrices.- 2.9a Matrix-variate Laplacian.- 2.9b The Density of S2i.- 2.9c A Particular Case.- Exercises.- 3 Quadratic and Bilinear Forms in Elliptically Contoured Distributions.- 3.0 Introduction.- 3.1 De£nitions and Basic Results.- 3.2 Moments of Quadratic Forms.- 3.3 The Distribution of Quadratic Forms.- 3.4 Noncentral Distribution.- 3.5 Quadratic Forms in Random Matrices.- 3.6 Quadratic Forms of Random Idempotent Matrices.- 3.7 Cochran’s Theorem.- 3.8 Test Statistics for Elliptically Contoured Distributions.- Sample Correlation Coefficient.- Likelihood Ratio Criteria.- Exercises.- 4 Zonal Polynomials.- 4.0 Introduction.- 4.1 Wishart Distribution.- 4.2 Symmetric Polynomials.- 4.3 Zonal Polynomials.- 4.4 Laplace Transform and Hypergeometric Function.- 4.5 Binomial Coefficients.- 4.6 Some Special Functions.- Exercises.- Table 4.3.2(a).- Table 4.3.2(b).- Table 4.4.1.- 5 Generalized Quadratic Forms.- 5.0 Introduction.- 5.1 A Representation of the Distribution of a Generalized Quadratic Form.- 5.2 An Alternate Representation.- 5.3 The Distribution of the Latent Roots of a Quadratic Form.- 5.4 Distributions of Some Functions of XAX’.- 5.5 Generalized Hotelling’s T02.- 5.6 Anderson’s Linear Discriminant Function.- 5.7 Multivariate Calibration.- 5.8 Asymptotic Expansions of the Distribution of a Quadratic Form.- Exercises.- Table 5.6.1.- Table 5.6.2.- Appendix Invariant Polynomials.- Appendix A. l Representation of a Group.- Appendix A.2 Integration of theRepresentation Matrix over the Orthogonal Group.- Glossary of Symbols.- Author Index.

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