Nonparametric tests for multivariate multi-sample locations based on data depth

ABSTRACT

Several nonparametric tests for multivariate multi-sample location problem are proposed in this paper. These tests are based on the notion of data depth, which is used to measure the centrality/outlyingness of a given point with respect to a given distribution or a data cloud. Proposed tests are completely nonparametric and implemented through the idea of permutation tests. Performance of the proposed tests is compared with existing parametric test and nonparametric test based on data depth. An extensive simulation study reveals that proposed tests are superior to the existing tests based on data depth with regard to power. Illustrations with real data are provided.

KEYWORDS:

• Data depth
• multivariate nonparametric tests
• permutation tests

AMS 1991 SUBJECT CLASSIFICATIONS:

• 62G10
• 62H15

Acknowledgement

Authors would like to thank an anonymous referee for their valuable comments and suggestions to improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors would like to thank Department of Science and Technology (DST), Science and Engineering Research Board (SERB), New Delhi for providing financial support under Extra Mural Research scheme (EMR/2017/167) to carry out the research work. The first author would like to thank Shivaji University, Kolhapur for the financial support under Research Initiation Scheme. This work is partially supported by the University Grants Commission (UGC), New Delhi, India under Special Assistance Programme and DST under FIST programme sanctioned to the Department.