4.0 Article

Non-parametric depth-based tests for the multivariate location problem

Journal

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS
Volume 63, Issue 2, Pages 309-330

Publisher

WILEY
DOI: 10.1111/anzs.12328

Keywords

central symmetry; depth function; location problem; permutation test; robustness

Funding

  1. Iran National Science Foundation

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Based on the concept of data depth, this paper describes two classes of affine invariant test statistics for the one-sample location problem, implemented through permutation tests. The tests perform well in simulation studies and have broader applicability compared to existing tests, making them competitive in performance.
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.

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