Geodesic
New integral nonparametric test for the hypothesis of affine symmetry
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 77-93

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The hypothesis of affine symmetry introduced by P. K. Sen in 1978 consists in the symmetry about the origin and in the same time in the independence of the components of two-dimensional random vector. New test statistic for testing this hypothesis is proposed. Some asymptotic properties of this statistic are investigated, in particular limiting distribution and large deviations. Bahadur local efficiency is also found and analyzed. Bibl. 18 titles. 
@article{ZNSL_1996_228_a7,
     author = {I. V. Gamov and Ya. Yu. Nikitin},
     title = {New integral nonparametric test for the hypothesis of affine symmetry},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--93},
     publisher = {mathdoc},
     volume = {228},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a7/}
}
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I. V. Gamov; Ya. Yu. Nikitin. New integral nonparametric test for the hypothesis of affine symmetry. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 77-93. http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a7/