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Asymptotic Optimality Of Likelihood Ratio Tests In Exponential Families
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Book Synopsis Asymptotic Optimality of Likelihood Ratio Tests in Exponential Families by : W. C. M. Kallenberg
Download or read book Asymptotic Optimality of Likelihood Ratio Tests in Exponential Families written by W. C. M. Kallenberg and published by . This book was released on 1978 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic oprimality of likelihood ratio tests in exponential families by : W. C. M. Kallenberg
Download or read book Asymptotic oprimality of likelihood ratio tests in exponential families written by W. C. M. Kallenberg and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotically Optimal Sequential Tests of Linear Hypotheses in Multiparameter Exponential Families by : Limin Zhang
Download or read book Asymptotically Optimal Sequential Tests of Linear Hypotheses in Multiparameter Exponential Families written by Limin Zhang and published by . This book was released on 1992 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Power of Likelihood Ratio Tests of Linear Hypotheses in Exponential Families by : William Vasek
Download or read book Asymptotic Power of Likelihood Ratio Tests of Linear Hypotheses in Exponential Families written by William Vasek and published by . This book was released on 1981 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Optimality Theory for Testing Problems with Restricted Alternatives by : T. A. B. Snijders
Download or read book Asymptotic Optimality Theory for Testing Problems with Restricted Alternatives written by T. A. B. Snijders and published by . This book was released on 1979 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic optimality theory for testing problems with restrict... by : Thomas Augustinus Benedictus Snijders
Download or read book Asymptotic optimality theory for testing problems with restrict... written by Thomas Augustinus Benedictus Snijders and published by . This book was released on 1979 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Likelihood-based Inference in Some Partially Non-regular Exponential Families by : Thomas Michael Dubinin
Download or read book Likelihood-based Inference in Some Partially Non-regular Exponential Families written by Thomas Michael Dubinin and published by . This book was released on 2000 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: For testing purposes the asymptotic independence allows separation of the leading terms in a Taylor expansion of the likelihood ratio test statistic for a point null hypothesis into two independent components, each of which is asymptotically X2 under the null hypothesis. The component associated with the estimator for the unknown lower threshold has two degrees of freedom. Hence if there are k "regular" parameters, the resulting test statistic will have an asymptotic distribution that is X[Superscript 2 over Subscript k + 2] (in contrast with the X[Superscript 2 over Subscript k + 1] null distribution that one would obtain if all parameters were regular). A number of Monte Carlo simulations demonstrate that our asymptotic results are applicable at moderate sample sizes. This holds true regardless whether the lower threshold is a censoring or a truncation point.
Book Synopsis Fundamentals of Statistical Exponential Families by : Lawrence D. Brown
Download or read book Fundamentals of Statistical Exponential Families written by Lawrence D. Brown and published by IMS. This book was released on 1986 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nearly Optimal Generalized Sequential Likelihood Ratio Tests in Multivariate Exponential Families by : Stanford University. Department of Statistics
Download or read book Nearly Optimal Generalized Sequential Likelihood Ratio Tests in Multivariate Exponential Families written by Stanford University. Department of Statistics and published by . This book was released on 1992 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Asymptotic Optimality Properties of Tests and Estimates in the Presence of Increasing Numbers of Nuisance Parameters by : Thomas Scott Hammerstrom
Download or read book On Asymptotic Optimality Properties of Tests and Estimates in the Presence of Increasing Numbers of Nuisance Parameters written by Thomas Scott Hammerstrom and published by . This book was released on 1978 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Statistical Inference by : Shailaja Deshmukh
Download or read book Asymptotic Statistical Inference written by Shailaja Deshmukh and published by Springer Nature. This book was released on 2021-07-05 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family, the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures, in particular, the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed, when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Wald’s test, their relationship with the likelihood ratio test and Karl Pearson’s chi-square test. An important finding is that, while testing any hypothesis about the parameters of a multinomial distribution, a score test statistic and Karl Pearson’s chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions, various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter, to motivate students towards solving these exercises and to enable digestion of the underlying concepts. The concepts from asymptotic inference are crucial in modern statistics, but are difficult to grasp in view of their abstract nature. To overcome this difficulty, keeping up with the recent trend of using R software for statistical computations, the book uses it extensively, for illustrating the concepts, verifying the properties of estimators and carrying out various test procedures. The last section of the chapters presents R codes to reveal and visually demonstrate the hidden aspects of different concepts and procedures. Augmenting the theory with R software is a novel and a unique feature of the book. The book is designed primarily to serve as a text book for a one semester introductory course in asymptotic statistical inference, in a post-graduate program, such as Statistics, Bio-statistics or Econometrics. It will also provide sufficient background information for studying inference in stochastic processes. The book will cater to the need of a concise but clear and student-friendly book introducing, conceptually and computationally, basics of asymptotic inference.
Book Synopsis Repeated Significance Tests for Exponential Families by : Inchi Hu
Download or read book Repeated Significance Tests for Exponential Families written by Inchi Hu and published by . This book was released on 1985 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report considered the significance levels and powers of repeates significance test (RTS). Typically these quantities cannot be calculated exactly and some sort of approximations are required. Satisfactory approximations of significance levels of RST for exponential families have been obtained by Lalley (1983) and Woodroofe (1978). In this report another method due to Siegmund (1985) in the special case of normal observations with known variance is developed. The main advantages that are claimed for this method are two-fold. First, it can be used to approximate the power of the RST. Second, it enables one to estimate both powers and significance levels of the modified RST. The approximations are also useful in determining confidence intervals. The proof of a nonlinear renewas theorem for conditional random walks and some numerical results are also given. Additional keywords: Distribution functions; Tables(data); Random walks; Null hypothesis case. (Author).
Book Synopsis Repeated Likelihood Ratio Tests for Curved Exponential Families by : Steven Paul Lalley
Download or read book Repeated Likelihood Ratio Tests for Curved Exponential Families written by Steven Paul Lalley and published by . This book was released on 1980 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of repeated significance tests for curved hypotheses in multiparameter exponential families is studied, and asymptotic formulae for the significance levels of such tests are obtained. Special attention is given the important case of comparing Bernoulli success probabilities. (Author).
Book Synopsis Asymptotic Theory of Testing Statistical Hypotheses by : Vladimir E. Bening
Download or read book Asymptotic Theory of Testing Statistical Hypotheses written by Vladimir E. Bening and published by Walter de Gruyter. This book was released on 2011-08-30 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Book Synopsis Principles of Signal Detection and Parameter Estimation by : Bernard C. Levy
Download or read book Principles of Signal Detection and Parameter Estimation written by Bernard C. Levy and published by Springer Science & Business Media. This book was released on 2008-07-07 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive and current understanding of signal detection and estimation, including problems and solutions for each chapter. Signal detection plays an important role in fields such as radar, sonar, digital communications, image processing, and failure detection. The book explores both Gaussian detection and detection of Markov chains, presenting a unified treatment of coding and modulation topics. Addresses asymptotic of tests with the theory of large deviations, and robust detection. This text is appropriate for students of Electrical Engineering in graduate courses in Signal Detection and Estimation.
Book Synopsis Asymptotic Optimal Inference for Non-ergodic Models by : I. V. Basawa
Download or read book Asymptotic Optimal Inference for Non-ergodic Models written by I. V. Basawa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains a comprehensive account of the recent work of the authors and other workers on large sample optimal inference for non-ergodic models. The non-ergodic family of models can be viewed as an extension of the usual Fisher-Rao model for asymptotics, referred to here as an ergodic family. The main feature of a non-ergodic model is that the sample Fisher information, appropriately normed, converges to a non-degenerate random variable rather than to a constant. Mixture experiments, growth models such as birth processes, branching processes, etc. , and non-stationary diffusion processes are typical examples of non-ergodic models for which the usual asymptotics and the efficiency criteria of the Fisher-Rao-Wald type are not directly applicable. The new model necessitates a thorough review of both technical and qualitative aspects of the asymptotic theory. The general model studied includes both ergodic and non-ergodic families even though we emphasise applications of the latter type. The plan to write the monograph originally evolved through a series of lectures given by the first author in a graduate seminar course at Cornell University during the fall of 1978, and by the second author at the University of Munich during the fall of 1979. Further work during 1979-1981 on the topic has resolved many of the outstanding conceptual and technical difficulties encountered previously. While there are still some gaps remaining, it appears that the mainstream development in the area has now taken a more definite shape.
Book Synopsis Likelihood Ratio Tests for Order Restrictions in Exponential Families by : Tim Robertson
Download or read book Likelihood Ratio Tests for Order Restrictions in Exponential Families written by Tim Robertson and published by . This book was released on 1975 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: