A Class of Weighted Rank Correlation Measures

• Autorzy: Sanatgar Majid , Dolati Ali , Amini Mohammad

Identyfikatory

DOI

10.37190/0208-4147.41.1.4

• Języki publikacji: EN

Abstrakty

EN

We propose a class of weighted rank correlation measures extending Spearman’s rho. This class consists of two types of measures. The first type, which extends Blest’s rank correlation, places more emphasis on the agreement in top ranks. The second one places more emphasis on the agreement in the bottom ranks. The asymptotic distribution of the proposed measures and some of their properties are studied. A simulation study is performed to compare the performance of the proposed statistics for testing independence by using asymptotic relative efficiency calculations.

Słowa kluczowe

EN

weighted rank correlation; copula; asymptotic distribution

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2021
• Tom: Vol. 41, Fasc. 1
• Strony: 39--54
• Opis fizyczny: Bibliogr. 21 poz., tab., wykr.

Twórcy

autor

Sanatgar Majid

• Department of Statistics, Yazd University, Yazd, Iran

autor

Dolati Ali

• Department of Statistics, Yazd University, Yazd, Iran

autor

Amini Mohammad

• Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran

Bibliografia

• [1] J. Behboodian, A. Dolati and M. Úbeda-Flores, Measures of association based on average quadrant dependence, J. Probab. Statist. Sci. 3 (2005), 161-173.
• [2] D. C. Blest, Rank correlation an alternative measure, Austral. New Zealand J. Statist. 42 (2000), 101-111.
• [3] T. Coolen-Maturi, A new weighted rank coefficient of concordance, J. Appl. Statist. 41 (2014), 1721-1745.
• [4] L. Dancelli, M. Manisera and M. Vezzoli, On two classes of weighted rank correlation measures deriving from the Spearman’s ρ, in: Statistical Models for Data Analysis, Springer, (2013), 107-114.
• [5] C. Genest and J. F. Plante, On Blest’s measure of rank correlation, Canad. J. Statist. 31 (2003), 35-52.
• [6] J. Hájek, A Course in Nonparametric Statistics, Holden-Day, San Francisco, 1969.
• [7] R. L. Iman and W. J. Conover, A measure of top-down correlation, Technometrics 29 (1987), 351-357.
• [8] M. Kendall, Rank Correlation Methods, Griffin, London, 1948.
• [9] P. Matula, A note on some inequalities for certain clases of positively dependent random variables, Probab. Math. Statist. 24 (2004), 17-26
• [10] T. A. Maturi and E. H. Abdelfattah, A new weighted rank correlation, J. Math. Statist. 4 (2008), 226-230.
• [11] R. B. Nelsen, An Introduction to Copulas, 2nd ed., Springer, New York, 2006.
• [12] Ya. Yu. Nikitin, Asymptotic Efficiency of Nonparametric Tests, Cambridge Univ. Press, 2009.
• [13] J. Pinto da Costa and C. Soares, A weighted rank measure of correlation, Austral. New Zealand J. Statist. 47 (2005), 515-529.
• [14] D. Quade and I. Salama, A survey of weighted rank correlation, in: Order Statistics and Nonparametrics: Theory and Applications, 1992, 213-224.
• [15] L. Rüschendorf, Asymptotic distributions of multivariate rank order statistics, Ann. Statist. 4 (1976), 912-923.
• [16] I. Salama and D. Quade, A nonparametric comparison of two multiple regressions by means of a weighted measure of correlation, Comm. Statist. Theory Methods 11 (1982), 1185-1195.
• [17] J. Segers, Asymptotics of empirical copula processes under non-restrictive smoothness assumptions, Bernoulli 18 (2012), 764-782.
• [18] G. S. Shieh, A weighted Kendall’s tau statistic, Statist. Probab. Lett. 39 (1998), 17-24.
• [19] Z. Šidák, P. K. Sen, and J. Hájek, Theory of Rank Tests, Academic Press, 1999.
• [20] A. Sklar, Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231.
• [21] A. W. van der Vaart and J. A. Wellner, Weak Convergence and Empirical Processes: with Applications to Statistics, Springer, New York, 1996.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).