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Author : Lawrence D. Brown
Publisher : IMS
Page : 302 pages
File Size : 40,9 Mb
Release : 1986
Category : Business & Economics
ISBN : 0940600102
Author : Lawrence D. Brown
Publisher : Unknown
Page : 284 pages
File Size : 47,5 Mb
Release : 2008*
Category : Exponential families (Statistics)
ISBN : OCLC:275471699
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 : O. Barndorff-Nielsen
Publisher : John Wiley & Sons
Page : 248 pages
File Size : 40,9 Mb
Release : 2014-05-07
Category : Mathematics
ISBN : 9781118857373
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 : Stefan Bedbur,Udo Kamps
Publisher : Springer Nature
Page : 147 pages
File Size : 40,7 Mb
Release : 2021-10-07
Category : Mathematics
ISBN : 9783030819002
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 : Rolf Sundberg
Publisher : Cambridge University Press
Page : 297 pages
File Size : 41,5 Mb
Release : 2019-08-29
Category : Business & Economics
ISBN : 9781108476591
A readable, digestible introduction to essential theory and wealth of applications, with a vast set of examples and numerous exercises.
Author : Ole E. Barndorff-Nielsen
Publisher : Unknown
Page : 238 pages
File Size : 47,6 Mb
Release : 1978
Category : Distribution (Probability theory)
ISBN : OCLC:30398003
Author : Yoel Haitovsky,Hans Rudolf Lerche,Ya'acov Ritov
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642574108
This volume is a collection of papers presented at a conference held in Shoresh Holiday Resort near Jerusalem, Israel, in December 2000 organized by the Israeli Ministry of Science, Culture and Sport. The theme of the conference was "Foundation of Statistical Inference: Applications in the Medical and Social Sciences and in Industry and the Interface of Computer Sciences". The following is a quotation from the Program and Abstract booklet of the conference. "Over the past several decades, the field of statistics has seen tremendous growth and development in theory and methodology. At the same time, the advent of computers has facilitated the use of modern statistics in all branches of science, making statistics even more interdisciplinary than in the past; statistics, thus, has become strongly rooted in all empirical research in the medical, social, and engineering sciences. The abundance of computer programs and the variety of methods available to users brought to light the critical issues of choosing models and, given a data set, the methods most suitable for its analysis. Mathematical statisticians have devoted a great deal of effort to studying the appropriateness of models for various types of data, and defining the conditions under which a particular method work. " In 1985 an international conference with a similar title* was held in Is rael. It provided a platform for a formal debate between the two main schools of thought in Statistics, the Bayesian, and the Frequentists.
Author : Masafumi Akahira
Publisher : Springer
Page : 122 pages
File Size : 49,7 Mb
Release : 2017-07-26
Category : Mathematics
ISBN : 9789811052965
This book presents new findings on nonregular statistical estimation. Unlike other books on this topic, its major emphasis is on helping readers understand the meaning and implications of both regularity and irregularity through a certain family of distributions. In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. This focus includes the (truncated) Pareto distribution, which is widely used in various fields such as finance, physics, hydrology, geology, astronomy, and other disciplines. The family is essential in that it links both regular and nonregular distributions, as it becomes a regular exponential family if the truncation parameter is known. The emphasis is on presenting new results on the maximum likelihood estimation of a natural parameter or truncation parameter if one of them is a nuisance parameter. In order to obtain more information on the truncation, the Bayesian approach is also considered. Further, the application to some useful truncated distributions is discussed. The illustrated clarification of the nonregular structure provides researchers and practitioners with a solid basis for further research and applications.
Author : Ole Barndorff-Nielsen
Publisher : Unknown
Page : 238 pages
File Size : 49,6 Mb
Release : 1978
Category : Electronic
ISBN : 0835733912
Author : Bradley Efron
Publisher : Cambridge University Press
Page : 264 pages
File Size : 55,8 Mb
Release : 2022-12-15
Category : Mathematics
ISBN : 9781108805438
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 : Bradley Efron
Publisher : Cambridge University Press
Page : 263 pages
File Size : 42,8 Mb
Release : 2022-12-15
Category : Computers
ISBN : 9781108488907
This accessible course on a central player in modern statistical practice connects models with methodology, without need for advanced math.
Author : Uwe Küchler,Michael Sorensen
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 42,5 Mb
Release : 2006-05-09
Category : Mathematics
ISBN : 9780387227658
A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.
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
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 : Frank Nielsen,Frank Critchley,Christopher T. J. Dodson
Publisher : Springer
Page : 299 pages
File Size : 47,6 Mb
Release : 2016-11-24
Category : Technology & Engineering
ISBN : 9783319470580
This book focuses on the application and development of information geometric methods in the analysis, classification and retrieval of images and signals. It provides introductory chapters to help those new to information geometry and applies the theory to several applications. This area has developed rapidly over recent years, propelled by the major theoretical developments in information geometry, efficient data and image acquisition and the desire to process and interpret large databases of digital information. The book addresses both the transfer of methodology to practitioners involved in database analysis and in its efficient computational implementation.
Author : Uwe Kuchler,Michael Sorensen
Publisher : Unknown
Page : 336 pages
File Size : 54,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475770995