Kendall's W reconsidered

Oliver Grothe (1) , Friedrich Schmid (1)

1 Department of Economic and Social Statistics

In their seminal paper, Kendall and Babington Smith (1939) suggested a measure W to quantify the agreement between d rankings of n objects. Its distribution was essentially investigated under the assumption of independent rankings. In many applications, however, the rankings are not independent. This paper reconsiders Kendall's W, investigating its distribution for dependent rankings using copula theory. We show that Kendall's W is asymptotically normally distributed under very weak assumptions and that its variance can be estimated by means of bootstrap and jackknife. We present an application of Kendall's W to returns and volatilities of the German DAX-30 assets.

Mots clés: Physical Sciences

Oliver Grothe, Friedrich Schmid. Kendall's W reconsidered. Communications in Statistics - Simulation and Computation, 2011, 40 (02), pp.297-317. ⟨10.1080/03610918.2010.538791⟩. ⟨hal-00657567⟩