Akahira M., Takeuchi K. Non-Regular Statistical Estimation

New York: Springer, 1995. — 191 p.In order to obtain many of the classical results in the theory of statistical estimation, it is usual to impose regularity conditions on the distributions under consideration. In small sample and large sample theories of estimation there are well established sets of regularity conditions, and it is worth while to examine what may follow if any one of these regularity conditions fail to hold. "Non-regular estimation" literally means the theory of statistical estimation when some or other of the regularity conditions fail to hold. In this monograph, the authors present a systematic study of the meaning and implications of regularity conditions, and show how the relaxation of such conditions can often lead to surprising conclusions. Their emphasis is on considering small sample results and to show how pathological examples may be considered in this broader framework.General Discussions on Unbiased Estimation
Lower Bound for the Variance of Unbiased Estimators
Amounts of Information and the Minimum Variance Unbiased Estimation
Loss of Information Associated with the Order Statistics and Related Estimators in the Case of Double Exponential Distributions
Estimation of a Common Parameter for Pooled Samples from the Uniform Distributions and the Double Exponential Distributions
Higher Order Asymptotics in Estimation for Two-Sided Weibull Type Distributions
“3/2-th” and Second Order Asymptotics of the Generalized Bayes Estimators for a Family of Truncated Distributions
Supplement The Bound for the Asymptotic Distribution of Estimators when the Maximum Order of Consistency Depends on the Parameter