Statistical Inference in Elliptically Contoured and Related Distributions

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: Statistical Inference in Elliptically Contoured and Related Distributions (): Fang, Kai-Tai, Anderson, T. W.: BooksCited by: Statistical inference in elliptically contoured and related distributions.

New York: Allerton Press, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Kai-Tang Fang; T W Anderson.

Statistical inference in elliptically contoured and related distributions / edited by Kai-Tai Fang and T.W. Anderson. QA S73 Stochastic orders and decision under risk /. The next three chapters are devoted to statistical inference.

Chapter 7 focuses on estimation results, whereas Chap.8 is concerned with hypothesis testing problems. Inference for linear models is studied in Chap Chapter 10 deals with the application of the elliptically contoured distributions Cited by: Elliptically Contoured Models in Statistics and Portfolio Theory fully revises the first detailed introduction to the theory of matrix variate elliptically contoured distributions.

There are two additional chapters, and all the original chapters of this classic text have been updated. Statistical Inference in Elliptically Contoured and Related Distributions STATISTICAL INFERENCE IN ELLIPTICALLY CONTOURED AND RELATED DISTRIBUTIONS Edited by Kai-Tai Fang, Institute of Applied Mathematics, Academia Sinica, Beijing, China and T.

Anderson, Department of Statistics, Stanford University, Stanford, CAUSA TABLE OF CONTENTS. Abstract: The class of elliptically contoured distributions, which includes multivariate t-distributions and contaminated normal distributions, serves as a useful generalization of the class of normal multivariate distributions.

The density, marginal and conditional densities, and moments of an elliptically contoured distribution are related in a simple fashion to those of a normal distribution. A.K. Gupta, T. Varga, "Some inference problems for matrix variate elliptically contoured distributions" Statistics, 26 () pp.

– [a10] A.K. Gupta, T. Varga, "Characterization of matrix variate elliptically contoured distributions", Adv. Theory and Practice of Statistics: A Volume in Honor of Samuel Kotz, Wiley () pp. – The book will be useful for researchers, teachers, and graduate students in statistics and related fields whose interests involve multivariate statistical analysis.

Parts of this book were presented by Arjun K Gupta as a one semester course at Bowling Green State University. Some new results have also been included which generalize the results. K.T. Fang, T.W. Anderson (Eds.), Statistical Inference in Elliptically Contoured and Related Distribution, Allerton Press, New York (), pp.

Statistical inference in simplicially contoured sample distributions Article in Metrika 56(3) November with 5 Reads How we measure 'reads'. Statistical Inference in Elliptically Contoured matrices under multivariate elliptically contoured distributions are discussed.

of related elliptical distributions are also derived with. The aim is to provide an overviewof the scientific domain of statistical inference without going in to minute details of any particular statistical method.

This is done by considering several commonly used multivariate models, following both normal and non-normal, including elliptically contoured, distributions for the responses. Plann.

Inference () –], both in the noninformative and conjugate prior cases. The first result gives inference robustness with respect to departures from the underlying distribution assumption in the direction of elliptically contoured distributions, even in. Statistical Inference in Elliptically Contoured and Related Distributions.

Allerton Press, New York. Allerton Press, New York. Mathematical Reviews (MathSciNet):. Symmetric multivariate and related distributions.

Monographs on statistics and applied probability. London: Chapman and Hall. ISBN OCLC CS1 maint: ref=harv ; Gupta, Arjun K.; Varga, Tamas; Bodnar, Taras ().

Elliptically contoured models in statistics and portfolio theory (2nd ed.). New York: Springer-Verlag. The class of matrix variate elliptically contoured distributions can be defined in many ways. Here the definition of A.K.

Gupta and T. Varga is given. A random matrix (see Matrix variate distribution) is said to have a matrix variate elliptically contoured distribution if its characteristic function has the form with a -matrix, a -matrix, a -matrix, a -matrix, and.

Statistical Inference in Elliptically Contoured and Related Distributions (with Kai-Tai Fang) (). Allerton Press, New York, vii+pp. Multivariate Analysis and Its Applications (with K.T.

Fang and I. Olkin) (). Institute of Mathematical Statistics, Hayward, California, xiv+pp. Books. The distributions of functions of random matrices with elliptically contoured distributions are discussed in Chapter 5, with special attention being paid to quadratic forms.

Characterization results are given in Chapter 6. Chapters are devoted to statistical inference. The class of elliptically contoured distributions, which includes multivariate t-distributions and contaminated normal distributions, serves as a useful generalization of the class of normal multivariate distributions.

The density, marginal and conditional densities, and moments of an elliptically contoured distribution are related in a simple fashion to those of a normal distribution.

Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more. Statistical inference in elliptically contoured and related distributions in SearchWorks catalog.

Author of An introduction to multivariate statistical analysis, Probability, statistics, and mathematics, Introduction to multivariate statistical analysis, The statistical analysis of time series, Statistical Inference in Elliptically Contoured and Related Distributions, The statistical analysis of time series, Multivariate analysis and its applications, A bibliography of multivariate.For elliptically contoured distributions, Uhas pdf h(u) = πp/2 Γ(p/2) kpu p/2−1g(u).() For c>0, an ECp(µ,cI,g) distribution is spherical about µ where I is the p×pidentity matrix.

The multivariate normal distribution Np(µ,Σ) has kp = (2π)−p/2,ψ(u) = g(u) = exp(−u/2) and h(u) is the χ2 p pdf. The following lemma is useful for proving properties of EC distributions.