Multivariate Exponential Families A Concise Guide To Statistical Inference

Author : Stefan Bedbur,Udo Kamps
Publisher : Springer Nature
Page : 147 pages
File Size : 49,5 Mb
Release : 2021-10-07
Category : Mathematics
ISBN : 9783030819002

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Multivariate Exponential Families: A Concise Guide to Statistical Inference by Stefan Bedbur,Udo Kamps Pdf

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.

Author : Bradley Efron
Publisher : Cambridge University Press
Page : 264 pages
File Size : 51,5 Mb
Release : 2022-12-15
Category : Mathematics
ISBN : 9781108805438

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Exponential Families in Theory and Practice by Bradley Efron Pdf

During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book connects exponential family theory with its applications in a way that doesn't require advanced mathematical preparation.

Author : Rolf Sundberg
Publisher : Cambridge University Press
Page : 297 pages
File Size : 46,5 Mb
Release : 2019-08-29
Category : Business & Economics
ISBN : 9781108476591

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Statistical Modelling by Exponential Families by Rolf Sundberg Pdf

A readable, digestible introduction to essential theory and wealth of applications, with a vast set of examples and numerous exercises.

Author : Lawrence D. Brown
Publisher : IMS
Page : 302 pages
File Size : 45,9 Mb
Release : 1986
Category : Business & Economics
ISBN : 0940600102

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Fundamentals of Statistical Exponential Families by Lawrence D. Brown Pdf

Author : O. Barndorff-Nielsen
Publisher : John Wiley & Sons
Page : 248 pages
File Size : 47,9 Mb
Release : 2014-05-07
Category : Mathematics
ISBN : 9781118857373

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Information and Exponential Families by O. Barndorff-Nielsen Pdf

First published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions.

Author : Martin J. Wainwright,Michael Irwin Jordan
Publisher : Now Publishers Inc
Page : 324 pages
File Size : 55,7 Mb
Release : 2008
Category : Computers
ISBN : 9781601981844

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Graphical Models, Exponential Families, and Variational Inference by Martin J. Wainwright,Michael Irwin Jordan Pdf

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.

Author : James K. Lindsey
Publisher : Oxford University Press
Page : 512 pages
File Size : 47,7 Mb
Release : 1996
Category : Mathematics
ISBN : 0198523599

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Parametric Statistical Inference by James K. Lindsey Pdf

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.

Author : Milind B. Bhatt
Publisher : Lulu.com
Page : 110 pages
File Size : 50,5 Mb
Release : 2024-06-14
Category : Electronic
ISBN : 9781329392755

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STATISTICAL INFERENCE FOR NON REGULAR FAMILY OF DISTRIBUTIONS (UNIFIED THEORY) by Milind B. Bhatt Pdf

Author : Bo-Cheng Wei
Publisher : Unknown
Page : 248 pages
File Size : 51,6 Mb
Release : 1998-09
Category : Mathematics
ISBN : UOM:39015043239618

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Exponential Family Nonlinear Models by Bo-Cheng Wei Pdf

This book gives a comprehensive introduction to exponential family nonlinear models, which are the natural extension of generalized linear models and normal nonlinear regression models. The differential geometric framework is presented for these models and geometric methods are widely used in this book. This book is ideally suited for researchers in statistical interfaces and graduate students with a basic knowledge of statistics.

Author : Masafumi Akahira
Publisher : Unknown
Page : 122 pages
File Size : 43,7 Mb
Release : 2017
Category : Mathematical statistics
ISBN : 9811052972

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Statistical Estimation for Truncated Exponential Families by Masafumi Akahira Pdf

Author : K. Balakrishnan
Publisher : Routledge
Page : 414 pages
File Size : 40,8 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351449113

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Exponential Distribution by K. Balakrishnan Pdf

The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon

Author : David J. Olive
Publisher : Springer
Page : 434 pages
File Size : 51,7 Mb
Release : 2014-05-07
Category : Mathematics
ISBN : 9783319049724

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Statistical Theory and Inference by David J. Olive Pdf

This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.

Author : Ole E. Barndorff-Nielsen
Publisher : Unknown
Page : 238 pages
File Size : 55,6 Mb
Release : 1978
Category : Distribution (Probability theory)
ISBN : OCLC:30398003

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Information and Exponential Families by Ole E. Barndorff-Nielsen Pdf

Author : Lawrence D. Brown
Publisher : Unknown
Page : 284 pages
File Size : 46,6 Mb
Release : 2008*
Category : Exponential families (Statistics)
ISBN : OCLC:275471699

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Fundamentals of Statistical Exponential Families by Lawrence D. Brown Pdf

This e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.

Author : Giri Narayan C
Publisher : World Scientific
Page : 180 pages
File Size : 41,9 Mb
Release : 1996-10-22
Category : Mathematics
ISBN : 9789814501644

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Group Invariance In Statistical Inference by Giri Narayan C Pdf

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.