New Characterization-Based Symmetry Tests

被引:19
作者
Bozin, Vladimir [1 ,2 ]
Milosevic, Bojana [1 ]
Nikitin, Ya. Yu. [3 ,4 ]
Obradovic, Marko [1 ]
机构
[1] Univ Belgrade, Fac Math, Studenski Trg 16, Belgrade, Serbia
[2] Math Inst SANU, Kneza Mihaila 36, Belgrade, Serbia
[3] St Petersburg State Univ, Dept Math & Mech, Univ Skaia Nab 7-9, St Petersburg 199034, Russia
[4] Natl Res Univ Higher Sch Econ, Souza Pechatnikov 16, St Petersburg 190008, Russia
关键词
Symmetry tests; Characterization; Degenerate U-statistics; Second-order Gaussian chaos process; Approximation of maximal eigenvalue; Asymptotic efficiency;
D O I
10.1007/s40840-018-0680-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Two new symmetry tests, of integral and Kolmogorov type, based on the characterization by squares of linear statistics are proposed. The test statistics are related to the family of degenerate U-statistics. Their asymptotic properties are explored. The maximal eigenvalue, needed for the derivation of their logarithmic tail behavior, was calculated or approximated using techniques from the theory of linear operators and the perturbation theory. The quality of the tests is assessed using the approximate Bahadur efficiency as well as the simulated powers. The tests are shown to be comparable with some recent and classical tests of symmetry.
引用
收藏
页码:297 / 320
页数:24
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