Theory of Statistical Estimation: Contributions to Higher Order Asymptotics and Non-Regular Cases

This book is a reconstruction of Masafumi Akahira’s works on statistical estimation and its related fields, especially higher order asymptotics and non-regular cases with consideration based on information amounts.There have been few books on higher order asymptotics and non-regular cases, but the book helps the reader to understand the meaning and implications of the hierarchical structure of higher order asymptotics and gives some insights into the structure of non-regular estimation.After the results on the second and third order asymptotic efficiency in the volume entitled “Joint Statistical Papers of Akahira and Takeuchi” are summarized, the positive resolution of the conjecture “third order efficiency implies fourth order efficiency” of J.K. Ghosh is described, from which the fourth order asymptotic efficiency of the bias-adjusted maximum likelihood estimator and the bias-adjusted generalized Bayes estimator is shown.In non-regular situations, the (maximum) order of consistency a