Exponential Families of Stochastic Processes
Exponential Families of Stochastic Processes

Author: Uwe Küchler

Publisher: Springer Science & Business Media

Published: 2006-05-09

Total Pages: 325

ISBN-13: 0387227652

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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.

Information and Exponential Families
Information and Exponential Families

Author: O. Barndorff-Nielsen

Publisher: John Wiley & Sons

Published: 2014-05-07

Total Pages: 248

ISBN-13: 1118857372

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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.

Multivariate Exponential Families: A Concise Guide to Statistical Inference
Multivariate Exponential Families: A Concise Guide to Statistical Inference

Author: Stefan Bedbur

Publisher: Springer Nature

Published: 2021-10-07

Total Pages: 147

ISBN-13: 3030819000

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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.