TY - JOUR

T1 - New Characterization-Based Symmetry Tests

AU - Bozin, Vladimir

AU - Milošević, Bojana

AU - Nikitin, Ya. Yu.

AU - Obradović, Marko

N1 - Publisher Copyright: © 2018, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Критерий Колмогорова

KW - симметрия

KW - эффективность

KW - большие уклонения

KW - test of symmetry

KW - limit distribution

KW - asymptotic efficiency

KW - characterization

KW - U-statistic

KW - Characterization

KW - Approximation of maximal eigenvalue

KW - Symmetry tests

KW - Second-order Gaussian chaos process

KW - Asymptotic efficiency

KW - Degenerate U-statistics

UR - https://link.springer.com/article/10.1007/s40840-018-0680-3?wt_mc=alerts.TOCjournals&utm_source=toc&utm_medium=email&utm_campaign=toc_40840_43_1

UR - http://www.scopus.com/inward/record.url?scp=85066978240&partnerID=8YFLogxK

U2 - 10.1007/s40840-018-0680-3

DO - 10.1007/s40840-018-0680-3

M3 - Article

VL - 43

SP - 297

EP - 320

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

SN - 0126-6705

IS - 1

ER -