Description

Book Synopsis

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.




Table of Contents

Introduction.- Parametrizations and Basic Properties.- Distributional and Statistical Properties.- Parameter Estimation.- Hypotheses Testing.- Exemplary Multivariate Applications.

Multivariate Exponential Families: A Concise Guide to Statistical Inference

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    A Paperback by Stefan Bedbur, Udo Kamps

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      Book details

      Publisher Springer Nature Switzerland AG
      Published 8 October 2021
      ISBN-13 9783030818999
      978-3030818999
      ISBN-10 3030818993
      Also in:
      Mathematics Probability and statistics

      Description

      Book Synopsis

      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.




      Table of Contents

      Introduction.- Parametrizations and Basic Properties.- Distributional and Statistical Properties.- Parameter Estimation.- Hypotheses Testing.- Exemplary Multivariate Applications.

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