Statistical Estimation for Truncated Exponential Families
Seiten
2017
|
1st ed. 2017
Springer Verlag, Singapore
978-981-10-5295-8 (ISBN)
Springer Verlag, Singapore
978-981-10-5295-8 (ISBN)
In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. 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.
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.
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.
Masafumi Akahira, Professor Emeritus, Institute of Mathematics, University of Tsukuba
Chapter I: One-sided truncated exponential family of distributions.- Chapter II: Two-sided truncated exponential family of distributions.
| Erscheinungsdatum | 16.08.2017 |
|---|---|
| Reihe/Serie | JSS Research Series in Statistics | SpringerBriefs in Statistics |
| Zusatzinfo | 10 Illustrations, black and white; XI, 122 p. 10 illus. |
| Verlagsort | Singapore |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra |
| Mathematik / Informatik ► Mathematik ► Statistik | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Wirtschaft | |
| Schlagworte | Maximum Likelihood Estimator • Natural Parameter • Second Order Asymptotic Loss • Truncated Exponential Family • Truncation Parameter |
| ISBN-10 | 981-10-5295-6 / 9811052956 |
| ISBN-13 | 978-981-10-5295-8 / 9789811052958 |
| Zustand | Neuware |
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