Tests for Two-Sample Location Problem Based on Subsample Quantiles
Affiliation(s)
Department of Statistics, Bangalore University, Bangalor, India. Department of Statistics, SDM College, Ujire, India. Department of Public Health Dentistry, SDM College of Dental Sciences and Hospital, Dharwad, India.
Department of Statistics, Bangalore University, Bangalor, India. Department of Statistics, SDM College, Ujire, India. Department of Public Health Dentistry, SDM College of Dental Sciences and Hospital, Dharwad, India.
ABSTRACT
This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests proposed is established. The asymptotic relative performance of the proposed class of test with respect to the optimal member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distributions.
Cite this paper
P. Pandit, S. Kumari and S. Javali, "Tests for Two-Sample Location Problem Based on Subsample Quantiles," Open Journal of Statistics, Vol. 4 No. 1, 2014, pp. 70-74. doi: 10.4236/ojs.2014.41007.
P. Pandit, S. Kumari and S. Javali, "Tests for Two-Sample Location Problem Based on Subsample Quantiles," Open Journal of Statistics, Vol. 4 No. 1, 2014, pp. 70-74. doi: 10.4236/ojs.2014.41007.
References
[1] J. Hajek and Z. Sidak, “Theory of Rank Tests,” Academic Press, New York, 1967. [2] J. V. Deshpande and S. C. Kochar, “Some Competitors of Wilcoxon-Mann Whitney Test for the Location Alternatives,” Journal of Indian Statistical Association, Vol. 19, 1982, pp. 9-18. [3] W. R. Stephenson and M. Gosh, “Two Sample Non-Parametric Tests Based on Subsamples,” Communications in Statistics— Theory and Methods, Vol. 14, No. 7, 1985, pp. 1669-1684. http://dx.doi.org/10.1080/03610928508829003 [4] E. L. Lehmann, “Consistency and Unbiasedness of Certain Nonparametric Tests,” Annals of Mathematical Statistics, Vol. 22, No. 2, 1951, pp. 165-179.
http://dx.doi.org/10.1214/aoms/1177729639 [5] H. B. Mann and D. R. Whitney, “On a Test of Whether One of Two Random Variables Is Stochastically Larger than the Other,” Annals of Mathematical Statistics, Vol. 18, No. 1, 1947, pp. 50-60.
http://dx.doi.org/10.1214/aoms/1177730491 [6] I. D. Shetty and Z. Govindarajulu, “A Two-Sample Test for Location,” Communications in Statistics—Theory and Methods, Vol. 17, No. 7, 1988, pp. 2389-2401.
http://dx.doi.org/10.1080/03610928808829752 [7] I. D. Shetty and S. V. Bhat, “A Note on the Generalization of Mathisen’s Median Test,” Statistics & Probability Letters, Vol. 19, No. 3, 1994, pp. 199-204.
http://dx.doi.org/10.1016/0167-7152(94)90105-8 [8] I. A. Ahmad, “A Class of Mann-Whitney-Wilcoxon Type Statistics,” The American Statistician, Vol. 50, No. 4, 1996, pp. 324-327. [9] J. Xie and C. E. Priere, “Generalizing the Mann-Whitney Wilcoxon Statistic,” Journal of Non-Parametric Statistics, Vol. 12, No. 5, 2000, pp. 661-682. http://dx.doi.org/10.1080/10485250008832827
[1] J. Hajek and Z. Sidak, “Theory of Rank Tests,” Academic Press, New York, 1967. [2] J. V. Deshpande and S. C. Kochar, “Some Competitors of Wilcoxon-Mann Whitney Test for the Location Alternatives,” Journal of Indian Statistical Association, Vol. 19, 1982, pp. 9-18. [3] W. R. Stephenson and M. Gosh, “Two Sample Non-Parametric Tests Based on Subsamples,” Communications in Statistics— Theory and Methods, Vol. 14, No. 7, 1985, pp. 1669-1684. http://dx.doi.org/10.1080/03610928508829003 [4] E. L. Lehmann, “Consistency and Unbiasedness of Certain Nonparametric Tests,” Annals of Mathematical Statistics, Vol. 22, No. 2, 1951, pp. 165-179.
http://dx.doi.org/10.1214/aoms/1177729639 [5] H. B. Mann and D. R. Whitney, “On a Test of Whether One of Two Random Variables Is Stochastically Larger than the Other,” Annals of Mathematical Statistics, Vol. 18, No. 1, 1947, pp. 50-60.
http://dx.doi.org/10.1214/aoms/1177730491 [6] I. D. Shetty and Z. Govindarajulu, “A Two-Sample Test for Location,” Communications in Statistics—Theory and Methods, Vol. 17, No. 7, 1988, pp. 2389-2401.
http://dx.doi.org/10.1080/03610928808829752 [7] I. D. Shetty and S. V. Bhat, “A Note on the Generalization of Mathisen’s Median Test,” Statistics & Probability Letters, Vol. 19, No. 3, 1994, pp. 199-204.
http://dx.doi.org/10.1016/0167-7152(94)90105-8 [8] I. A. Ahmad, “A Class of Mann-Whitney-Wilcoxon Type Statistics,” The American Statistician, Vol. 50, No. 4, 1996, pp. 324-327. [9] J. Xie and C. E. Priere, “Generalizing the Mann-Whitney Wilcoxon Statistic,” Journal of Non-Parametric Statistics, Vol. 12, No. 5, 2000, pp. 661-682. http://dx.doi.org/10.1080/10485250008832827