Statistical Estimation for Truncated Exponential Families

This book presents new insights into nonregular statistical estimation, focusing on truncated exponential families, including the Pareto distribution, and their implications for researchers.

This book delves into the intricacies of nonregular statistical estimation, specifically focusing on a truncated exponential family of distributions. The authors present new findings that highlight the significance of both regularity and irregularity in statistical analysis. By exploring the natural and truncation parameters, the book aims to equip readers with a deeper understanding of these concepts, particularly in the context of maximum likelihood estimation when one of the parameters is treated as a nuisance parameter.

Statistical Estimation for Truncated Exponential Families emphasizes the importance of the truncated Pareto distribution, which finds applications across various fields such as finance, physics, hydrology, and astronomy. This distribution serves as a bridge between regular and nonregular families, demonstrating that it can become a regular exponential family if the truncation parameter is known. The authors provide new insights into the estimation processes, ensuring that readers grasp the implications of these statistical methods.

Additionally, the book discusses the Bayesian approach to gaining more information about truncation, offering practical applications to useful truncated distributions. By illustrating the nonregular structure, the authors provide researchers and practitioners with a robust foundation for future exploration and application of these statistical concepts. Overall, Statistical Estimation for Truncated Exponential Families serves as a valuable resource for those looking to deepen their understanding of nonregular statistical estimation.