Large deviation behavior of estimators for flattened distributions in a middle part (Probability Models and Statistical Inferences)

Abstract

From the viewpoint of large deviation, the Bahadur efficiency based on the information inequality for the tail probability of estimators is well known in the asymptotic theory of estimation. On the other hand, the large deviation efficiency up to the second order was introduced in Akahira (2006, 2010) from a different viewpoint from the Bahadur efficiency. In this article, from the latter viewpoint, the lower bound for the large deviation probability for asymptotically median unbiased estimators is obtained for flattened distributions in a middle part, which do not belong to an exponential family. The influence of the flat part of distributions on the bound with its relation to the large deviation efficiency is investigated.