Geodesic
Asymptotic efficiency of new distribution-free tests of symmetry for generalized skew alternatives
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 82-101

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We calculate Bahadur efficiency of new nonparametric tests for symmetry recently proposed by Nikitin and Ahsanullah [30]. In contrast with that paper where only location alternatives were discussed, we are interested in generalized skew alternatives. It is shown that the new tests are highly efficient for a vast class of skew alternatives. The problem of most favorable alternatives is also explored. 
@article{ZNSL_2016_454_a3,
     author = {G. T. Bookiya and Ya. Yu. Nikitin},
     title = {Asymptotic efficiency of new distribution-free tests of symmetry for generalized skew alternatives},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {82--101},
     publisher = {mathdoc},
     volume = {454},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a3/}
}
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G. T. Bookiya; Ya. Yu. Nikitin. Asymptotic efficiency of new distribution-free tests of symmetry for generalized skew alternatives. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 82-101. http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a3/