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Distribution and Dependence-Function Estimation for Bivariate Extreme-Value Distributions

Peter Hall and Nader Tajvidi
Bernoulli
Vol. 6, No. 5 (Oct., 2000), pp. 835-844
DOI: 10.2307/3318758
Stable URL: http://www.jstor.org/stable/3318758
Page Count: 10
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Distribution and Dependence-Function Estimation for Bivariate Extreme-Value Distributions
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Abstract

Two new methods are suggested for estimating the dependence function of a bivariate extreme-value distribution. One is based on a multiplicative modification of an earlier technique proposed by Pickands, and the other employs spline smoothing under constraints. Both produce estimators that satisfy all the conditions that define a dependence function, including convexity and the restriction that its curve lie within a certain triangular region. The first approach does not require selection of smoothing parameters; the second does, and for that purpose we suggest explicit tuning methods, one of them based on cross-validation.

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