Authors: Božin, Vladimir 
Milošević, Bojana
Nikitin, Ya Yu
Obradović, Marko
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: New Characterization-Based Symmetry Tests
Journal: Bulletin of the Malaysian Mathematical Sciences Society
Volume: 43
Issue: 1
First page: 297
Last page: 320
Issue Date: 1-Jan-2020
Rank: M21
ISSN: 0126-6705
DOI: 10.1007/s40840-018-0680-3
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.
Keywords: Approximation of maximal eigenvalue | Asymptotic efficiency | Characterization | Degenerate U-statistics | Second-order Gaussian chaos process | Symmetry tests
Publisher: Springer Link
Project: Analysis and algebra with applications 
Geometry, Education and Visualization With Applications 

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