Advances and Applications in Statistics
Volume 5, Issue 2, Pages 209 - 227
(August 2005)
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MEASURING ASYMPTOTIC DEPENDENCE OF EXTREMES AND TESTS BASED ON TAIL INDEXES
Chang C. Y. Dorea (Brazil)
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Abstract: Let x1, x2, ? be i.i.d. random vectors on W̼/span> Rd and let f and g be real-valued functions on W. Define Xj = f(xj) and Yj = g(xj)and assume that the joint distribution of (Xj, Yj) belongs to the domain of attraction of the bivariate maximal extreme value distribution G with marginals and where gf > 0 and gg > 0 are thecorresponding tail indexes. We introduce probability measures on the set of extreme points Wf and Wg and derive tests for asymptotic dependence of X(n) = max{X1, ?, X?n}and Y(n) = max{Y1, ?, Y?n} based on Hill?s estimates of gf and gg. |
Keywords and phrases: tail index, bivariate extreme distribution, asymptotic independence. |
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