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Author : Narayan C. Giri
Publisher : [Hamilton, Ont.] : Selecta Statistica Canadiana
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.:/5 (25 download)
Download or read book Invariance and Minimax Statistical Tests written by Narayan C. Giri and published by [Hamilton, Ont.] : Selecta Statistica Canadiana. This book was released on 1976 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Narayan C. Giri
Publisher : World Scientific
ISBN 13 : 9789810218751
Total Pages : 188 pages
Book Rating : 4.2/5 (187 download)
Download or read book Group Invariance in Statistical Inference written by Narayan C. Giri and published by World Scientific. This book was released on 1996 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: In applied and pure sciences, the structural properties of groups are increasingly utilised to find better solutions in statistical sciences. Modern computers make statistical methods with large numbers of variables feasible. Invariance is a mathematical term for symmetry, and many statistical problems exhibit such properties. In statistical analysis with large numbers of variables, the invariance approach is becoming increasingly popular and useful because of its ability and usefulness in deriving better statistical procedures.In this book, Multivariate Statistical Inference is presented through Invariance.
Author : Narayan C. Giri
Publisher :
ISBN 13 :
Total Pages : 101 pages
Book Rating : 4.:/5 (265 download)
Download or read book Invariance and Minimax Tests written by Narayan C. Giri and published by . This book was released on 1971 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Narayan C Giri
Publisher : World Scientific
ISBN 13 : 9814501646
Total Pages : 178 pages
Book Rating : 4.8/5 (145 download)
Download or read book Group Invariance In Statistical Inference written by Narayan C Giri and published by World Scientific. This book was released on 1996-10-22 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: In applied and pure sciences, the structural properties of groups are increasingly utilised to find better solutions in statistical sciences. Modern computers make statistical methods with large numbers of variables feasible. Invariance is a mathematical term for symmetry, and many statistical problems exhibit such properties. In statistical analysis with large numbers of variables, the invariance approach is becoming increasingly popular and useful because of its ability and usefulness in deriving better statistical procedures.In this book, Multivariate Statistical Inference is presented through Invariance.
Author : J. K. Ghosh
Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.3/5 (91 download)
Download or read book Invariance in Testing and Estimation written by J. K. Ghosh and published by . This book was released on 1967 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Morris L. Eaton
Publisher : IMS
ISBN 13 : 9780940600157
Total Pages : 148 pages
Book Rating : 4.6/5 (1 download)
Download or read book Group Invariance Applications in Statistics written by Morris L. Eaton and published by IMS. This book was released on 1989 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Narayan C. Giri
Publisher : Academic Press
ISBN 13 : 1483263339
Total Pages : 336 pages
Book Rating : 4.4/5 (832 download)
Download or read book Multivariate Statistical Inference written by Narayan C. Giri and published by Academic Press. This book was released on 2014-07-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate Statistical Inference is a 10-chapter text that covers the theoretical and applied aspects of multivariate analysis, specifically the multivariate normal distribution using the invariance approach. Chapter I contains some special results regarding characteristic roots and vectors, and partitioned submatrices of real and complex matrices, as well as some special theorems on real and complex matrices useful in multivariate analysis. Chapter II deals with the theory of groups and related results that are useful for the development of invariant statistical test procedures, including the Jacobians of some specific transformations that are useful for deriving multivariate sampling distributions. Chapter III is devoted to basic notions of multivariate distributions and the principle of invariance in statistical testing of hypotheses. Chapters IV and V deal with the study of the real multivariate normal distribution through the probability density function and through a simple characterization and the maximum likelihood estimators of the parameters of the multivariate normal distribution and their optimum properties. Chapter VI tackles a systematic derivation of basic multivariate sampling distributions for the real case, while Chapter VII explores the tests and confidence regions of mean vectors of multivariate normal populations with known and unknown covariance matrices and their optimum properties. Chapter VIII is devoted to a systematic derivation of tests concerning covariance matrices and mean vectors of multivariate normal populations and to the study of their optimum properties. Chapters IX and X look into a treatment of discriminant analysis and the different covariance models and their analysis for the multivariate normal distribution. These chapters also deal with the principal components, factor models, canonical correlations, and time series. This book will prove useful to statisticians, mathematicians, and advance mathematics students.
Author : James Berger
Publisher : Springer Science & Business Media
ISBN 13 : 147571727X
Total Pages : 440 pages
Book Rating : 4.4/5 (757 download)
Download or read book Statistical Decision Theory written by James Berger and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decision theory is generally taught in one of two very different ways. When of opti taught by theoretical statisticians, it tends to be presented as a set of mathematical techniques mality principles, together with a collection of various statistical procedures. When useful in establishing the optimality taught by applied decision theorists, it is usually a course in Bayesian analysis, showing how this one decision principle can be applied in various practical situations. The original goal I had in writing this book was to find some middle ground. I wanted a book which discussed the more theoretical ideas and techniques of decision theory, but in a manner that was constantly oriented towards solving statistical problems. In particular, it seemed crucial to include a discussion of when and why the various decision prin ciples should be used, and indeed why decision theory is needed at all. This original goal seemed indicated by my philosophical position at the time, which can best be described as basically neutral. I felt that no one approach to decision theory (or statistics) was clearly superior to the others, and so planned a rather low key and impartial presentation of the competing ideas. In the course of writing the book, however, I turned into a rabid Bayesian. There was no single cause for this conversion; just a gradual realization that things seemed to ultimately make sense only when looked at from the Bayesian viewpoint.
Author : Erich L. Lehmann
Publisher : Springer Science & Business Media
ISBN 13 : 038727605X
Total Pages : 795 pages
Book Rating : 4.3/5 (872 download)
Download or read book Testing Statistical Hypotheses written by Erich L. Lehmann and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 795 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760.
Author : Narayan C. Giri
Publisher : CRC Press
ISBN 13 : 1482276372
Total Pages : 583 pages
Book Rating : 4.4/5 (822 download)
Download or read book Multivariate Statistical Analysis written by Narayan C. Giri and published by CRC Press. This book was released on 2003-11-14 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significantly revised and expanded, Multivariate Statistical Analysis, Second Edition addresses several added topics related to the properties and characterization of symmetric distributions, elliptically symmetric multivariate distributions, singular symmetric distributions, estimation of covariance matrices, tests of mean against one-sided altern
Author : Oscar Wesler
Publisher :
ISBN 13 :
Total Pages : 98 pages
Book Rating : 4.F/5 ( download)
Download or read book A Modified Minimax Principle written by Oscar Wesler and published by . This book was released on 1955 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Erik Torgersen
Publisher : Cambridge University Press
ISBN 13 : 9780521250306
Total Pages : 706 pages
Book Rating : 4.2/5 (53 download)
Download or read book Comparison of Statistical Experiments written by Erik Torgersen and published by Cambridge University Press. This book was released on 1991-03-14 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.
Author : A.F. Siegel
Publisher : Routledge
ISBN 13 : 1351457632
Total Pages : 336 pages
Book Rating : 4.3/5 (514 download)
Download or read book Counterexamples in Probability And Statistics written by A.F. Siegel and published by Routledge. This book was released on 2017-11-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.
Author : Shanti Swarup Gupta
Publisher :
ISBN 13 : 9783540905721
Total Pages : 104 pages
Book Rating : 4.9/5 (57 download)
Download or read book Multiple Statistical Decision Theory written by Shanti Swarup Gupta and published by . This book was released on 1981 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some auxiliary results: monotonicity properties of probability distributions; Multiple decision theory: a general approach; Modified minimax decision procedures; Invariant decision procedures; Robust selection procedures: most economical multiple decision rules; Multiple decision procedures based on tests.
Author : Thomas S. Ferguson
Publisher : Academic Press
ISBN 13 : 1483221237
Total Pages : 409 pages
Book Rating : 4.4/5 (832 download)
Download or read book Mathematical Statistics written by Thomas S. Ferguson and published by Academic Press. This book was released on 2014-07-10 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Statistics: A Decision Theoretic Approach presents an investigation of the extent to which problems of mathematical statistics may be treated by decision theory approach. This book deals with statistical theory that could be justified from a decision-theoretic viewpoint. Organized into seven chapters, this book begins with an overview of the elements of decision theory that are similar to those of the theory of games. This text then examines the main theorems of decision theory that involve two more notions, namely the admissibility of a decision rule and the completeness of a class of decision rules. Other chapters consider the development of theorems in decision theory that are valid in general situations. This book discusses as well the invariance principle that involves groups of transformations over the three spaces around which decision theory is built. The final chapter deals with sequential decision problems. This book is a valuable resource for first-year graduate students in mathematics.
Author : Takeaki Kariya
Publisher : Academic Press
ISBN 13 : 1483266001
Total Pages : 208 pages
Book Rating : 4.4/5 (832 download)
Download or read book Robustness of Statistical Tests written by Takeaki Kariya and published by Academic Press. This book was released on 2014-05-10 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robustness of Statistical Tests provides a general, systematic finite sample theory of the robustness of tests and covers the application of this theory to some important testing problems commonly considered under normality. This eight-chapter text focuses on the robustness that is concerned with the exact robustness in which the distributional or optimal property that a test carries under a normal distribution holds exactly under a nonnormal distribution. Chapter 1 reviews the elliptically symmetric distributions and their properties, while Chapter 2 describes the representation theorem for the probability ration of a maximal invariant. Chapter 3 explores the basic concepts of three aspects of the robustness of tests, namely, null, nonnull, and optimality, as well as a theory providing methods to establish them. Chapter 4 discusses the applications of the general theory with the study of the robustness of the familiar Student's r-test and tests for serial correlation. This chapter also deals with robustness without invariance. Chapter 5 looks into the most useful and widely applied problems in multivariate testing, including the GMANOVA (General Multivariate Analysis of Variance). Chapters 6 and 7 tackle the robust tests for covariance structures, such as sphericity and independence and provide a detailed description of univariate and multivariate outlier problems. Chapter 8 presents some new robustness results, which deal with inference in two population problems. This book will prove useful to advance graduate mathematical statistics students.
Author : Helmut Strasser
Publisher : Walter de Gruyter
ISBN 13 : 3110850826
Total Pages : 505 pages
Book Rating : 4.1/5 (18 download)
Download or read book Mathematical Theory of Statistics written by Helmut Strasser and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
