Overview
- Provides a basis for further research on estimation and presents applications to selected nonregular situations
- Clarifies the asymptotic difference between regular and nonregular structures through maximum likelihood and Bayesian estimation
- Serves as a research resource and fundamental tool for practitioners in statistical inference and related fields
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)
Part of the book sub series: JSS Research Series in Statistics (JSSRES)
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Table of contents (6 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Statistical Estimation for Truncated Exponential Families
Authors: Masafumi Akahira
Series Title: SpringerBriefs in Statistics
DOI: https://doi.org/10.1007/978-981-10-5296-5
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2017
Softcover ISBN: 978-981-10-5295-8Published: 02 August 2017
eBook ISBN: 978-981-10-5296-5Published: 26 July 2017
Series ISSN: 2191-544X
Series E-ISSN: 2191-5458
Edition Number: 1
Number of Pages: XI, 122
Number of Illustrations: 10 b/w illustrations
Topics: Statistical Theory and Methods, Statistics and Computing/Statistics Programs, Statistics for Business, Management, Economics, Finance, Insurance, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences