Nikitin, Ya Yu
|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||Abstract:||
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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