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Non‐parametric depth‐based tests for the multivariate location problem
Author(s) -
Dehghan Sakineh,
Faridrohani Mohammad Reza
Publication year - 2021
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12328
Subject(s) - mathematics , parametric statistics , multivariate statistics , affine transformation , nonparametric statistics , statistical hypothesis testing , permutation (music) , robustness (evolution) , statistics , algorithm , biochemistry , physics , chemistry , acoustics , gene , pure mathematics
Summary In this paper, using the notion of data depth, we describe two classes of affine invariant test statistics for the one‐sample location problem. The tests are implemented through the idea of permutation tests. The performance of the test against some competitors is investigated with an extensive simulation study. It is observed that the tests perform well when compared to their competitors for a wide spectrum of alternatives. If the proposed test is defined based on a moment‐free depth function, then it is not inherently required to have finite moments of any order and the tests have broader applicability than some of the existing tests. The robustness property of the proposed tests is considered with a simulation study. Finally, we apply the tests to a real data example.