Extremes of nonexchangeability
Tóm tắt
For identically distributed random variables X and Y with joint distribution function H, we show that the supremum of |H(x,y)-H(y,x)| is 1/3. Using copulas, we define a measure of nonexchangeability, and study maximally nonexchangeable random variables and copulas. In particular, we show that maximally nonexchangeable random variables are negatively correlated in the sense of Spearman's rho.
Tài liệu tham khảo
Galambos J (1982) Exchangeability, in Encyclopedia of Statistical Sciences, Vol. 2, Kotz, S and Johnson NL, editors. John Wiley & Sons, New York, 573–577
Lancaster HO (1963) Correlation and complete dependence of random variables. Ann. Math. Statist. 34, 1315–1321
Nelsen, RB (1999) An Introduction to Copulas. Springer, New York
Schweizer, B, Wolff, EF (1981) On nonparametric measures of dependence for random variables. Ann. Statist. 9, 870–885