Local Asymptotic Normality for Progressively Censored Likelihood Ratio Statistics and Applications

摘要

Several investigations were made of the notion of local asymptotic normality (LAN) of a family of probability distributions. The usefulness of this concept in problems of the theory of asymptotic estimation and hypothesis testing was demonstrated. A comprehensive examination of sets of conditions can be found ensuring the LAN for different families of probability distributions. Much attention has been focused on distributions connected with sequences of independent and identically distributed (iid) observations or those associated with a homogeneous Markov chain. In this paper conditions are presented ensuring the LAN for distributions connected with certain observations, which are neither independent nor identically distributed, when a class of stopping variables is incorporated in a natural way into the basic framework.