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.
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:
Download or read book Invariant Measures on Groups and Their Use in Statistics written by Robert A. Wijsman and published by IMS. This book was released on 1990 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Statistical Inference written by Anthony Almudevar and published by CRC Press. This book was released on 2021-12-30 with total page 1059 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume, presenting a formal theory of statistical inference. Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory.
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
Download or read book Theory of Statistical Inference written by Anthony Almudevar and published by CRC Press. This book was released on 2021-12-30 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume, presenting a formal theory of statistical inference. Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory.
Download or read book Principles of Statistical Inference written by Luigi Pace and published by World Scientific. This book was released on 1997-08-05 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term ?neo-Fisherian? highlights this.After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.
Download or read book Advances in Kinetic Theory and Computing written by B. Perthame and published by World Scientific. This book was released on 1994 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This selection of 8 papers discusses ?Equations of Kinetic Physics? with emphasis on analysis, modelling and computing. The first 3 papers are on numerical methods for Vlasov-Poisson and Vlasov-Maxwell Equations ? Comparison between Particles and Eulerian Methods (G Manfredi and M R Feix), Computing BGK Instability with Eulerian Codes (M R Feix, Pertrand & A Ghieco) and Coupling Particles and Eulerian Methods (S Mas-Gallic and P A Raviart) ? Followed by a survey of kinetic and macroscopic models for semiconductor devices ? Boltzmann Equation, Drift-Diffusion Models (F Poupaud). In addition, there are 2 papers on the modelling and analysis of singular perturbation problems arising in plasma physics ? Derivation of the Child-Lagmuyr Emission Laws (P Degond) and Euler Models with Small Pressure Terms (F Bouchut) ? followed by two papers on the analysis and numerical analysis of the Boltzmann equations ? Symmetry Properties in the Polynomials Arising in Chapman-Enskog Expansion (L Desvillettes and F Golse) and A General Introduction to Computing the Boltzmann Equations with Random Particle Methods (B Perthame).
Download or read book STATISTICAL INFERENCE written by M. RAJAGOPALAN and published by PHI Learning Pvt. Ltd.. This book was released on 2012-07-08 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended as a text for the postgraduate students of statistics, this well-written book gives a complete coverage of Estimation theory and Hypothesis testing, in an easy-to-understand style. It is the outcome of the authors’ teaching experience over the years. The text discusses absolutely continuous distributions and random sample which are the basic concepts on which Statistical Inference is built up, with examples that give a clear idea as to what a random sample is and how to draw one such sample from a distribution in real-life situations. It also discusses maximum-likelihood method of estimation, Neyman’s shortest confidence interval, classical and Bayesian approach. The difference between statistical inference and statistical decision theory is explained with plenty of illustrations that help students obtain the necessary results from the theory of probability and distributions, used in inference.
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.
Download or read book Statistical Inference Testing Of Hypotheses written by Srivastava & Srivastava and published by PHI Learning Pvt. Ltd.. This book was released on 2009-12 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: it emphasizes on J. Neyman and Egon Pearson's mathematical foundations of hypothesis testing, which is one of the finest methodologies of reaching conclusions on population parameter. Following Wald and Ferguson's approach, the book presents Neyman-Pearson theory under broader premises of decision theory resulting into simplification and generalization of results. On account of smooth mathematical development of this theory, the book outlines the main result on Lebesgue theory in abstract spaces prior to rigorous theoretical developments on most powerful (MP), uniformly most powerful (UMP) and UMP unbiased tests for different types of testing problems. Likelihood ratio tests their large sample properties to variety of testing situations and connection between confidence estimation and testing of hypothesis have been discussed in separate chapters. The book illustrates simplification of testing problems and reduction in dimensionality of class of tests resulting into existence of an optimal test through the principle of sufficiency and invariance. It concludes with rigorous theoretical developments on non-parametric tests including their optimality, asymptotic relative efficiency, consistency, and asymptotic null distribution.
Download or read book Philosophical Problems of Statistical Inference written by T. Seidenfeld and published by Springer Science & Business Media. This book was released on 1979-08-31 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and inverse inference; Neyman-Pearson theory; Fisherian significance testing; The fiducial argument: one parameter; The fiducial argument: several parameters; Ian hacking's theory; Henry Kyburg's theory; Relevance and experimental design.
Download or read book Recent Developments in Nonparametric Inference and Probability written by and published by IMS. This book was released on 2006 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book STATISTICAL INFERENCE THEORY OF ESTIMATION written by MANOJ KUMAR SRIVASTAVA and published by PHI Learning Pvt. Ltd.. This book was released on 2014-04-03 with total page 817 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is sequel to a book Statistical Inference: Testing of Hypotheses (published by PHI Learning). Intended for the postgraduate students of statistics, it introduces the problem of estimation in the light of foundations laid down by Sir R.A. Fisher (1922) and follows both classical and Bayesian approaches to solve these problems. The book starts with discussing the growing levels of data summarization to reach maximal summarization and connects it with sufficient and minimal sufficient statistics. The book gives a complete account of theorems and results on uniformly minimum variance unbiased estimators (UMVUE)—including famous Rao and Blackwell theorem to suggest an improved estimator based on a sufficient statistic and Lehmann-Scheffe theorem to give an UMVUE. It discusses Cramer-Rao and Bhattacharyya variance lower bounds for regular models, by introducing Fishers information and Chapman, Robbins and Kiefer variance lower bounds for Pitman models. Besides, the book introduces different methods of estimation including famous method of maximum likelihood and discusses large sample properties such as consistency, consistent asymptotic normality (CAN) and best asymptotic normality (BAN) of different estimators. Separate chapters are devoted for finding Pitman estimator, among equivariant estimators, for location and scale models, by exploiting symmetry structure, present in the model, and Bayes, Empirical Bayes, Hierarchical Bayes estimators in different statistical models. Systematic exposition of the theory and results in different statistical situations and models, is one of the several attractions of the presentation. Each chapter is concluded with several solved examples, in a number of statistical models, augmented with exposition of theorems and results. KEY FEATURES • Provides clarifications for a number of steps in the proof of theorems and related results., • Includes numerous solved examples to improve analytical insight on the subject by illustrating the application of theorems and results. • Incorporates Chapter-end exercises to review student’s comprehension of the subject. • Discusses detailed theory on data summarization, unbiased estimation with large sample properties, Bayes and Minimax estimation, separately, in different chapters.
Download or read book Statistical Decision Theory written by F. Liese and published by Springer Science & Business Media. This book was released on 2008-12-30 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: For advanced graduate students, this book is a one-stop shop that presents the main ideas of decision theory in an organized, balanced, and mathematically rigorous manner, while observing statistical relevance. All of the major topics are introduced at an elementary level, then developed incrementally to higher levels. The book is self-contained as it provides full proofs, worked-out examples, and problems. The authors present a rigorous account of the concepts and a broad treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory. With its broad coverage of decision theory, this book fills the gap between standard graduate texts in mathematical statistics and advanced monographs on modern asymptotic theory.
Download or read book Statistical Inference from Genetic Data on Pedigrees written by Elizabeth Alison Thompson and published by IMS. This book was released on 2000 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation While this monograph is not about show dogs or cats, its statistical methods could be applied to tracing the pedigree of these species as well as humans. Thompson (U. of Washington) covers such topics as genetic models, population allele frequencies, kinship/inbreeding coefficients, and Monte Carlo estimation. Includes supporting tables and figures. Suitable as a supplementary text or primary text for advanced students. Lacks an index. c. Book News Inc.
Download or read book Algebraic Methods in Statistics and Probability written by Marlos A. G. Viana and published by American Mathematical Soc.. This book was released on 2001 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 23 papers report recent developments in using the technique to help clarify the relationship between phenomena and data in a number of natural and social sciences. Among the topics are a coordinate-free approach to multivariate exponential families, some rank-based hypothesis tests for covariance structure and conditional independence, deconvolution density estimation on compact Lie groups, random walks on regular languages and algebraic systems of generating functions, and the extendibility of statistical models. There is no index. c. Book News Inc.
