publication . Preprint . 2015

On the Kendall Correlation Coefficient

Stepanov, Alexei;
Open Access English
  • Published: 06 Jul 2015
In the present paper, we first discuss the Kendall rank correlation coefficient. In continuous case, we define the Kendall rank correlation coefficient in terms of the concomitants of order statistics, find the expected value of the Kendall rank correlation coefficient and show that the later is free of n. We also prove that in continuous case the Kendall correlation coefficient converges in probability to its expected value. We then propose to consider the expected value of the Kendall rank correlation coefficient as a new theoretical correlation coefficient which can be an alternative to the classical Pearson product-moment correlation coefficient. At the end ...
free text keywords: Mathematics - Statistics Theory
Download from

Bairamov, I. and Stepanov, A. (2010). Numbers of near-maxima for the bivariate case, Statistics & Probability Letters, 80, 196-205.

Bhattacharya, B.B. (1974). Convergence of sample paths of normalized sums of induced order statistics, Ann. Statist. , 2, 1034-1039. [OpenAIRE]

Bhattacharya, B.B. (1984). Induced order statistics: theory and applications, In Handbook of Statistics 4, Ed. Krishnaiah, P. R. andSen, P. K., North Holland, Amsterdam, 383-403.

Chu, S.J., Huang, W.J. and Chen, H. (1999). A study of asymptotic distributions of concomitants of certain order statistics, Statist. Sinica, 9, 811-830.

Daniels, H. E. (1950). Rank correlation and population models, Journal of the Royal Statistical Society, Ser. B, 12 (2), 171-191.

David, H.A. (1994). Concomitants of Extreme Order Statistics, In Extreme Value Theory and Applications, Proceedings of the Conference on Extreme Value Theory and Applications, 1, Ed. Galambos, J., Lechner, J., and Simiu, E., Kluwer Academic Publishers, Boston 211-224.

David, H.A. and Galambos, J. (1974). The asymptotic theory of concomitants of order statistics, J. Appl. Probab., 11, 762-770.

David, H.A. and Nagaraja, H.N. (2003). Order Statistics, Third edition, John Wiley & Sons, NY.

Durbin J. and Stuart, A. (1951). Inversions and rank correlation coefficients, Journal of the Royal Statistical Society, Ser. B 13 (2), 303-309.

Egorov, V. A. and Nevzorov, V. B. (1984). Rate of convergence to the Normal law of sums of induced order statistics, Journal of Soviet Mathematics (New York), 25, 1139-1146.

Fisher, R. A. (1921). On the probable error of a coefficient of correlation deduced from a small sample, Metron, 1, 3-32.

Goel, P. K. and Hall, P. (1994). On the average difference between concomitants and order statistics, Ann. Probab., 22, 126-144. [OpenAIRE]

Kendall, M. G. (1970). Rank Correlation Methods, London, Griffin.

Xu, W., Hou, Y., Hung, Y. S. and Zou, Y. (2009). Comparison of Spearmans rho and Kendalls tau in Normal and Contaminated Normal Models, arXiv:1011.2009v1 [cs.IT].

Any information missing or wrong?Report an Issue