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.
References
- Chaudhuri P (1996). On a geometric notion of quantiles for multivariate data, Journal of the American Statistical Association, 91, 862-872. https://doi.org/10.1080/01621459.1996.10476954
- Chavan AR and Shirke DT (2020). Nonparametric two sample tests for scale parameters of multivariate distributions, Communications for Statistical Applications and Methods, 27, 397-412. https://doi.org/10.29220/CSAM.2020.27.4.397
- Chenouri S, Small CG, and Farrar TJ (2011). Data depth-based nonparametric scale tests, Canadian Journal of Statistics, 39, 356-369. https://doi.org/10.1002/cjs.10099
- Dovoedo YH and Chakraborti S (2015). Power of depth-based nonparametric tests for multivariate locations, Journal of Statistical Computation and Simulation, 85, 1987-2006. https://doi.org/10.1080/00949655.2014.913045
- Efron B and Tibshirani RJ (1994). An Introduction to the Bootstrap, CRC press, London.
- Gastwirth JL (1965). Percentile modifications of two sample rank tests, Journal of the American Statistical Association, 60, 1127-1141. https://doi.org/10.1080/01621459.1965.10480856
- Jolicoeur P and Mosimann JE (1960). Size and shape variation in the painted turtle. A principal component analysis, Growth, 24, 339-354.
- Li J and Liu RY (2004). New nonparametric tests of multivariate locations and scales using data depth, Statistical Science, 19, 686-696. https://doi.org/10.1214/088342304000000594
- Li J and Liu RY (2016). New nonparametric tests for comparing multivariate scales using data depth, In Robust Rank-Based and Nonparametric Methods (pp. 209-226), Springer, Michigan, USA.
- Liu RY (1990). On a notion of data depth based on random simplices, The Annals of Statistics, 18, 405-414. https://doi.org/10.1214/aos/1176347507
- Liu RY and Singh K (1993). A quality index based on data depth and multivariate rank tests, Journal of the American Statistical Association, 88, 252-260. https://doi.org/10.1080/01621459.1993.10594317
- Liu RY, Parelius JM, and Singh K (1999). Multivariate analysis by data depth: Descriptive statistics, graphics and inference, (with discussion and a rejoinder by liu and singh), The Annals of Statistics, 27, 783-858. https://doi.org/10.1214/aos/1018031259
- Liu RY and Singh K (2006). Rank tests for multivariate scale difference based on data depth, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 72, 17-36. https://doi.org/10.1090/dimacs/072/02
- Mahalanobis PC (1936). On the generalized distance in statistics, National Institute of Science of India, 1936.
- Pawar SD and Shirke DT (2019). Nonparametric tests for multivariate locations based on data depth, Communications in Statistics-Simulation and Computation, 48, 753-776. https://doi.org/10.1080/03610918.2017.1397165
- Rousseeuw PJ and Hubert M (1999). Regression depth, Journal of the American Statistical Association, 94, 388-402. https://doi.org/10.1080/01621459.1999.10474129
- Rousson V (2002). On distribution-free tests for the multivariate two-sample location-scale model, Journal of Multivariate Analysis, 80, 43-57. https://doi.org/10.1006/jmva.2000.1981
- 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 (pp. 25-38), Birkhauser, Basel.
- 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 (pp. 25-38), Birkhauser, Basel.
- Shirke DT and Khorate SD (2018). Two-Sample nonparametric test for testing equality of locations based on data depth, Journal of the Indian Society for Probability and Statistics, 19, 9-23. https://doi.org/10.1007/s41096-017-0031-y
- Singh K (1991). A notion of majority depth, Unpublished document, 1991.
- Tukey JW (1975). Mathematics and the picturing of data, In Proceedings of the International Congress of Mathematicians, Vancouver, 2, 523-531.
- Zuo Y and Serfling R (2000). General notions of statistical depth function, Annals of Statistics, 28, 461-482. https://doi.org/10.1214/aos/1016218226
- Zuo Y (2003). Projection-Based depth functions and associated medians, The Annals of Statistics, 31, 1460-1490. https://doi.org/10.1214/aos/1065705115