Download or read book On the Statistical Inference for Infinite Parameter Exponential Families written by B. L. S. Prakasa Rao and published by . This book was released on 1984 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Aspects of Statistical Inference written by A. H. Welsh and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relevant, concrete, and thorough--the essential data-based text onstatistical inference The ability to formulate abstract concepts and draw conclusionsfrom data is fundamental to mastering statistics. Aspects ofStatistical Inference equips advanced undergraduate and graduatestudents with a comprehensive grounding in statistical inference,including nonstandard topics such as robustness, randomization, andfinite population inference. A. H. Welsh goes beyond the standard texts and expertly synthesizesbroad, critical theory with concrete data and relevant topics. Thetext follows a historical framework, uses real-data sets andstatistical graphics, and treats multiparameter problems, yet isultimately about the concepts themselves. Written with clarity and depth, Aspects of Statistical Inference: * Provides a theoretical and historical grounding in statisticalinference that considers Bayesian, fiducial, likelihood, andfrequentist approaches * Illustrates methods with real-data sets on diabetic retinopathy,the pharmacological effects of caffeine, stellar velocity, andindustrial experiments * Considers multiparameter problems * Develops large sample approximations and shows how to use them * Presents the philosophy and application of robustness theory * Highlights the central role of randomization in statistics * Uses simple proofs to illuminate foundational concepts * Contains an appendix of useful facts concerning expansions,matrices, integrals, and distribution theory Here is the ultimate data-based text for comparing and presentingthe latest approaches to statistical inference.
Download or read book Estimation in Truncated Exponential Family of Distributions written by Laxman M. Hegde and published by . This book was released on 1986 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Principles of Statistical Inference written by D. R. Cox and published by Cambridge University Press. This book was released on 2006-08-10 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The mathematics is kept as elementary as feasible, though previous knowledge of statistics is assumed. The book will be valued by every user or student of statistics who is serious about understanding the uncertainty inherent in conclusions from statistical analyses.
Download or read book Essential Statistical Inference written by Dennis D. Boos and published by Springer Science & Business Media. This book was released on 2013-02-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for students and researchers who have had a first year graduate level mathematical statistics course. It covers classical likelihood, Bayesian, and permutation inference; an introduction to basic asymptotic distribution theory; and modern topics like M-estimation, the jackknife, and the bootstrap. R code is woven throughout the text, and there are a large number of examples and problems. An important goal has been to make the topics accessible to a wide audience, with little overt reliance on measure theory. A typical semester course consists of Chapters 1-6 (likelihood-based estimation and testing, Bayesian inference, basic asymptotic results) plus selections from M-estimation and related testing and resampling methodology. Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State. Their research has been eclectic, often with a robustness angle, although Stefanski is also known for research concentrated on measurement error, including a co-authored book on non-linear measurement error models. In recent years the authors have jointly worked on variable selection methods.
Download or read book Statistical Modelling by Exponential Families written by Rolf Sundberg and published by Cambridge University Press. This book was released on 2019-08-29 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters.
Download or read book Parametric Statistical Inference written by James K. Lindsey and published by Oxford University Press. This book was released on 1996 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two unifying components of statistics are the likelihood function and the exponential family. These are brought together for the first time as the central themes in this book on statistical inference, written for advanced undergraduate and graduate students in mathematical statistics.
Download or read book Graphical Models Exponential Families and Variational Inference written by Martin J. Wainwright and published by Now Publishers Inc. This book was released on 2008 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of this paper is a general set of variational principles for the problems of computing marginal probabilities and modes, applicable to multivariate statistical models in the exponential family.
Download or read book Bulletin Institute of Mathematical Statistics written by Institute of Mathematical Statistics and published by . This book was released on 1994 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Theory of Statistical Inference for Time Series written by Masanobu Taniguchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.
Download or read book Model Adequacy Tests for Exponential Family Regression Models written by Champa Hemanthi Magalla and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of testing for lack of fit in exponential family regression models is considered. Such nonlinear models are the natural extension of Normal nonlinear regression models and generalized linear models. As is usually the case, inadequately specified models have an adverse impact on statistical inference and scientific discovery. Models of interest are curved exponential families determined by a sequence of predictor settings and mean regression function, considered as a sub-manifold of the full exponential family. Constructed general alternative models are based on clusterings in the mean parameter components and allow likelihood ratio testing for lack of fit associated with the mean, equivalently natural parameter, for a proposed null model. A maximin clustering methodology is defined in this context to determine suitable clusterings for assessing lack of fit. In addition, a geometrically motivated goodness of fit test statistic for exponential family regression based on the information metric is introduced. This statistic is applied to the cases of logistic regression and Poisson regression, and in both cases it can be seen to be equal to a form of the Pearson [chi]2 statistic. This same statement is true for multinomial regression. In addition, the problem of testing for equal means in a heteroscedastic Normal model is discussed. In particular, a saturated 3 parameter exponential family model is developed which allows for equal means testing with unequal variances. A simulation study was carried out for the logistic and Poisson regression models to investigate comparative performance of the likelihood ratio test, the deviance test and the goodness of fit test based on the information metric. For logistic regression, the Hosmer-Lemeshow test was also included in the simulations. Notably, the likelihood ratio test had comparable power with that of the Hosmer-Lemeshow test under both m- and n-asymptotics, with superior power for constructed alternatives. A distance function defined between densities and based on the information metric is also given. For logistic models, as the natural parameters go to plus or minus infinity, the densities become more and more deterministic and limits of this distance function are shown to play an important role in the lack of fit analysis. A further simulation study investigated the power of a likelihood ratio test and a geometrically derived test based on the information metric for testing equal means in heteroscedastic Normal models.
Download or read book Multivariate Exponential Families A Concise Guide to Statistical Inference written by Stefan Bedbur and published by Springer Nature. This book was released on 2021-10-07 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise introduction to exponential families. Parametric families of probability distributions and their properties are extensively studied in the literature on statistical modeling and inference. Exponential families of distributions comprise density functions of a particular form, which enables general assertions and leads to nice features. With a focus on parameter estimation and hypotheses testing, the text introduces the reader to distributional and statistical properties of multivariate and multiparameter exponential families along with a variety of detailed examples. The material is widely self-contained and written in a mathematical setting. It may serve both as a concise, mathematically rigorous course on exponential families in a systematic structure and as an introduction to Mathematical Statistics restricted to the use of exponential families.
Download or read book Connected at infinity II a selection of mathematics by Indians written by Rajendra Bhatia and published by Springer. This book was released on 2013-01-01 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Statistics for Mathematicians written by Victor M. Panaretos and published by Birkhäuser. This book was released on 2016-06-01 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a coherent introduction to the main concepts and methods of one-parameter statistical inference. Intended for students of Mathematics taking their first course in Statistics, the focus is on Statistics for Mathematicians rather than on Mathematical Statistics. The goal is not to focus on the mathematical/theoretical aspects of the subject, but rather to provide an introduction to the subject tailored to the mindset and tastes of Mathematics students, who are sometimes turned off by the informal nature of Statistics courses. This book can be used as the basis for an elementary semester-long first course on Statistics with a firm sense of direction that does not sacrifice rigor. The deeper goal of the text is to attract the attention of promising Mathematics students.
Download or read book Exponential Families and Conditioning written by Ole E. Barndorff-Nielsen and published by . This book was released on 1973 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
