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.

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

Autorentext
Masafumi Akahira, Professor Emeritus, Institute of Mathematics, University of Tsukuba

Inhalt
Chapter I: One-sided truncated exponential family of distributions.- Chapter II: Two-sided truncated exponential family of distributions.