Dependence of non-continuous random variables
Dependence of non-continuous random variables
Dependence of non-continuous random variables
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Fallacies <strong>Dependence</strong> Concordance Measures Problems & References AppendixLess Sharp Bounds for Kendall’s Tau and Spearman’s Rho1. |˜τ(X,Y )| ≤ √ 1 − E ∆F 1 (X) √ 1 − E∆F 2 (Y ). The boundsare attained if Y = T(X) a.s. where T is a strictly monotoneand <strong>continuous</strong> transformation on the range <strong>of</strong> X.2. |˜ρ(X,Y )| ≤ √ 1 − E ∆F 1 (X) 2√ 1 − E ∆F 2 (Y ) 2 . The boundsare attained if Y = T(X) a.s. where T is a strictly monotoneand <strong>continuous</strong> transformation on the range <strong>of</strong> X.J. Nešlehová ETH Zurich<strong>Dependence</strong> <strong>of</strong> <strong>non</strong>-<strong>continuous</strong> <strong>random</strong> <strong>variables</strong>
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