[Author]
 Nazarov, A. I.; Tchirina, A. V.

[Title]
 On the available local asymptotic efficiency of some goodness-of-fit criteria

[AMS Subj-class]
 62G10 Nonparametric hypothesis testing
 49K15 Optimality conditions for problems involving ordinary differential equations
 62G20 Asymptotic properties of nonparametric inference

[Keywords]
 goodness–of–fit test, local Bahadur optimality, obstacle problem

[Abstract]
 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.

[Comments]
 LaTeX, Russian, 17 pp.

[Contact e-mail]
 al.il.nazarov@gmail.com