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

Research Article
  • 15 Downloads

Abstract

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.

Keywords

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

Notes

Acknowledgements

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)).

References

  1. Chenouri S, Small CG (2012) A nonparametric multivariate multisample test based on data depth. Electron J Stat 6:760–782MathSciNetCrossRefMATHGoogle Scholar
  2. Dovoedo YH, Chakraborti S (2015) Power of depth-based nonparametric tests for multivariate locations. J Stat Comput Simul 85(10):1987–2006MathSciNetCrossRefMATHGoogle Scholar
  3. Efron B, Tibshirani RJ (1994) An introduction to the bootstrap. CRC Press, Boca RatonMATHGoogle Scholar
  4. Jolicoeur P, Mosimann JE (1960) Size and shape variation in the painted turtle. A principal component analysis. Growth 24(4):339–354Google Scholar
  5. Li J, Liu RY (2004) New nonparametric tests of multivariate locations and scales using data depth. Stat Sci 19:686–696MathSciNetCrossRefMATHGoogle Scholar
  6. Liu RY (1990) On a notion of data depth based on random simplices. Ann Stat 18(1):405–414MathSciNetCrossRefMATHGoogle Scholar
  7. Liu RY (1995) Control charts for multivariate processes. J Am Stat Assoc 90(432):1380–1387MathSciNetCrossRefMATHGoogle Scholar
  8. Liu RY, Singh K (1993) A quality index based on data depth and multivariate rank tests. J Am Stat Assoc 88(421):252–260MathSciNetMATHGoogle Scholar
  9. Liu RY, Parelius JM, Singh K (1999) Multivariate analysis by data depth: descriptive statistics, graphics and inference, (with discussion and a rejoinder by Liu and Singh). Ann Stat 27(3):783–858CrossRefMATHGoogle Scholar
  10. Rousson V (2002) On distribution-free tests for the multivariate two-sample location-scale model. J Multivar Anal 80(1):43–57MathSciNetCrossRefMATHGoogle Scholar
  11. Serfling R (2002) A depth function and a scale curve based on spatial quantiles. In: Statistical data analysis based on the L1-norm and related methods, Birkhuser, Basel, pp 25–38Google Scholar
  12. Tukey JW (1975) Mathematics and the picturing of data. In: Proceedings of the international congress of mathematicians, vol 2, pp 523–531Google Scholar
  13. Zuo Y, Serfling R (2000) General notions of statistical depth function. Ann Stat 28:461–482MathSciNetCrossRefMATHGoogle Scholar

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

Personalised recommendations