Two-Sample Nonparametric Test for Testing Equality of Locations Based on Data Depth

  • Digambar T. Shirke
  • Swapnil Dattatray Khorate
Research Article


In the recent years, the notion of data depth has been widely used in multivariate data analysis since it measures the centrality or outlyingness of the multivariate data points with respect to the given data cloud and it orders the data from center to outward in any direction called ‘center-outward ordering’. In the present work, we propose a nonparametric test for testing equality of location parameter of two multivariate distributions using notion of data depth. The proposed test is motivated from the concept of correlation. We compare powers of the proposed test with existing tests for multivariate symmetric and skewed distributions through simulation. The proposed test gives an attractive powers against various alternatives. Application to a real life data is also provided.


Data depth Hotelling \(T^2\) test Permutation test Multivariate skewed distributions 



Both the authors are thankful to University Grants Commission, New Delhi for providing financial assistance to carry out the research work under Special Assistance Programme (F.520/8/DRS-I/2016(SAP-I)).


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Copyright information

© The Indian Society for Probability and Statistics (ISPS) 2018

Authors and Affiliations

  • Digambar T. Shirke
    • 1
  • Swapnil Dattatray Khorate
    • 1
  1. 1.Department of StatisticsShivaji UniversityKolhapurIndia

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