Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Depth-Based rank test for multivariate two-sample scale problem

  • Received : 2022.01.06
  • Accepted : 2023.02.23
  • Published : 2023.05.31
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Abstract

In this paper, a depth-based nonparametric test for a multivariate two-sample scale problem is proposed. The proposed test statistic is based on the depth-induced ranks and is thus distribution-free. In this article, the depth values of data points of one sample are calculated with respect to the other sample or distribution and vice versa. A comprehensive simulation study is used to examine the performance of the proposed test for symmetric as well as skewed distributions. Comparison of the proposed test with the existing depth-based nonparametric tests is accomplished through empirical powers over different depth functions. The simulation study admits that the proposed test outperforms existing nonparametric depth-based tests for symmetric and skewed distributions. Finally, an actual life data set is used to demonstrate the applicability of the proposed test.

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Acknowledgement

The first author would like to thank Department of Science and technology, Science and Engineering Research Board (DST-SERB), New Delhi for providding financial support under Extra Mural Research scheme (EMR/2017/167) to carry out the research work. The second author would like to thank Shivaji University, Kolhapur for the financial support under Research Initiation Scheme 2019-2020.

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