Geodesic
On the available local asymptotic efficiency of some goodness-of-fit criteria
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 218-235

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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. 
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     author = {A. I. Nazarov and A. V. Tchirina},
     title = {On the available local asymptotic efficiency of some goodness-of-fit criteria},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {218--235},
     publisher = {mathdoc},
     volume = {501},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a14/}
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A. I. Nazarov; A. V. Tchirina. On the available local asymptotic efficiency of some goodness-of-fit criteria. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 218-235. http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a14/