Multivariate ranks based on randomized lift-interdirections

0564920 - ÚTIA 2023 RIV NL eng J - Článek v odborném periodiku
Hudecová, Š. - Šiman, Miroslav
Multivariate ranks based on randomized lift-interdirections.
Computational Statistics and Data Analysis. Roč. 172, č. 1 (2022), č. článku 107480. ISSN 0167-9473. E-ISSN 1872-7352
Grant CEP: GA ČR GA21-05325S
Grant ostatní: GA ČR(CZ) GF22-01639K
Institucionální podpora: RVO:67985556
Klíčová slova: multivariate rank * lift-interdirection * interdirection * rank test * one-sample test * robustness
Obor OECD: Statistics and probability
Impakt faktor: 1.8, rok: 2022
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2022/SI/siman-0564920.pdf https://www.sciencedirect.com/science/article/pii/S0167947322000603?via%3Dihub

Every multivariate sign and rank test needs a workable concept of ranks for multivariate data. Unfortunately, multidimensional spaces lack natural ordering and, consequently, there are no universally accepted ways how to rank vector observations. Existing proposals usable beyond small dimensions are very few in number, and each of them has its own advantages and drawbacks. Therefore, new multivariate ranks based on randomized lift-interdirections are presented, discussed and investigated. These naturally robust and invariant hyperplane-based ranks can be computed quickly and easily even in relatively high-dimensional spaces, and they can be used for nonparametric statistical inference in some existing optimal statistical procedures without altering their asymptotic behavior under null hypotheses or changing their performance under local alternatives. This is not only proved theoretically in case of the canonical sign and rank one-sample test for elliptically distributed observations, but also illustrated empirically in a small simulation study.
Trvalý link: https://hdl.handle.net/11104/0336508