A CLASS OF TWO-SAMPLE SCALE TESTS BASED ON U-STATISTICS
DOI:
https://doi.org/10.29121/granthaalayah.v7.i9.2019.569Keywords:
Empirical Power, Pitman ARE, Scale Problem, Two-Sample, U-StatisticsAbstract [English]
A class of tests based on U-statistic is proposed for two-sample scale problem. The U-statistic is function of extremes of subsamples taken from random samples of two absolutely continuous distributions. The asymptotic distribution, null distribution and efficacy of the class of tests are studied. A comparison of its performance with respect to other tests is studied in terms of Pitman ARE and small sample performance through its empirical power. Application of the class of tests is illustrated through an example.
Downloads
References
Bhat, S. V. Studies in Nonparametric Inference, An unpublished Ph.D. thesis submitted to the Karnatak University, Dharwad, 1995.
Bhat, S. V., Shindhe, S. D. and Joshi, V. B. A Class of Outlier Resistant Tests for Two-sample Scale Problem, International Journal of Agricultural and Statistical Sciences. 14 (2), 2018, 455-463.
Bhat, S. V. and Shindhe, S. D. Distribution-free Tests Based on Subsample Maxima or Minima for Two-sample Scale Problem, Bulletin of Mathematics and Statistics Research. 7 (3), 2019, 20-35.
Deshpande, J. V., Gore, A. P. and Shanubhogue, A. Statistical Analysis of Nonnormal Data, New Age International Publishers Limited, Wiley Eastern Limited; 1995, 48.
Deshpande, J. V. and Kusum, K. A Test for Nonparametric Two-sample Scale Problem, Australian Journal of Statistics. 32, 1984, 16-24. DOI: https://doi.org/10.1111/j.1467-842X.1984.tb01263.x
Duran, B. S. A Survey of Nonparametric Tests for Scale, Communications in Statistics Theory and Methods. 5(14), 1976, 1287-1312. DOI: https://doi.org/10.1080/03610927608827443
Kusum, K. A New Distribution-free Test for Two-sample Scale Problem. Journal of Indian Statistical Association, 23, 1985, 97-107.
Kochar C. S. and Gupta R. P. Some Competitors of the Mood Test for the Two-sample Scale Problem, Communications in Statistics Theory and Methods, 15(1), 1986, 231-239. DOI: https://doi.org/10.1080/03610928608829117
Kossler, W. and Narinder Kumar, An Adaptive Test for the Two-sample Scale Problem Where the Common Quantile may be Different from the Median, Statistical Methodology, 29, 2016, 10-17. DOI: https://doi.org/10.1016/j.stamet.2015.08.001
Lehmann, E. L. Consistency and Unbiasedness of Certain Nonparametric Tests, Annals of Mathematical Statistics, 22, 1951, 165-179. DOI: https://doi.org/10.1214/aoms/1177729639
Mahajan, K. K., Gaur, A. and Arora, A. A Nonparametric Test for a Two Sample Scale Problem Based on Subsample Medians, Statistics and Probability Letters, 81, 2011, 983-988. DOI: https://doi.org/10.1016/j.spl.2011.01.018
Mehra K. L. and Rao K. S. A Class of Two-sample Nonparametric Tests for Scale Based on Sub-sample Extrema, In: 80th Indian Science Congress conference held at Goa University, Goa, India, 1992.
Mood, A. M. On the Asymptotic Efficiency of Certain Nonparametric Two-sample Tests, Annals of Mathematical Statistics, 25, 1954, 514-533. DOI: https://doi.org/10.1214/aoms/1177728719
Narinder Kumar and Goyal, M. A General Class of Nonparametric Tests for Comparing Scale Parameters, Communications in Statistics Theory and Methods, 47 (24), 2018, 5956-5972. DOI: https://doi.org/10.1080/03610926.2017.1404099
Rohatgi, V. K. and Saleh, A. K. M. E. An Introduction to Probability and statistics, 2 Ed., John Wiley and Sons, Inc; 2001. DOI: https://doi.org/10.1002/9781118165676
Siegel, S. and Tukey, J. W. A Nonparametric Sum of Ranks Procedure for Relative Spread in Unpaired Samples, Journal of American Statistical Association, 55, 1960, 429-444. DOI: https://doi.org/10.1080/01621459.1960.10482073
Shetty, I. D. and Bhat, S. V. A Class of Distribution-free Tests for the Two-sample Scale Problem. In: Proceedings of II International symposium on Optimization and Statistics held at Aligarh Muslim University, Aligarh, India, Nov 2-4, 1993, 91-96.
Shetty, I. D. and Pandit, P. V. A Note on a New Class of Distribution-free Tests for the Two Sample Scale Problem Based on Subsample Medians, Communications in Statistics Theory and Methods, 33, 2004, 2271-2280. DOI: https://doi.org/10.1081/STA-200026632
Sukhatme, B. V. On Certain Two-sample Nonparametric Tests for Variances, Annals of Mathematical Statistics, 28, 1957, 188-194. DOI: https://doi.org/10.1214/aoms/1177707046
Sukhatme, B. V. A Two-sample Distribution-free Test for Comparing Variances, Biometrika, 45, 1958, 544-548. DOI: https://doi.org/10.1093/biomet/45.3-4.544
Downloads
Published
How to Cite
Issue
Section
License
With the licence CC-BY, authors retain the copyright, allowing anyone to download, reuse, re-print, modify, distribute, and/or copy their contribution. The work must be properly attributed to its author.
It is not necessary to ask for further permission from the author or journal board.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.
