On the Available Local Asymptotic Efficiency of some Goodness-of-fit Criteria

摘要

The concept of local asymptotic Bahadur optimality for a sequence of statistics is well known. The following problem was posed, and in many cases solved, by Ya. Yu. Nikitin: to describe the class of distributions for which a given sequence of statistics is locally asymptotically optimal against specific alternatives (shift, scale, etc.). However, in some cases, this problem has no solution. We propose to consider a modified problem. Its solution gives the value of the available asymptotic efficiency of the corresponding statistics.