Hall, Peter; Tajvidi, Nader Distribution and dependence-function estimation for bivariate extreme-value distributions. (English) Zbl 1067.62540 Bernoulli 6, No. 5, 835-844 (2000). Summary: 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. Cited in 1 ReviewCited in 45 Documents MSC: 62G32 Statistics of extreme values; tail inference 62G07 Density estimation Keywords:convex hull; cross-validation; marginal distribution; multivariate extreme-value distribution; nonparametric curve estimation; smoothing parameter; spline PDFBibTeX XMLCite \textit{P. Hall} and \textit{N. Tajvidi}, Bernoulli 6, No. 5, 835--844 (2000; Zbl 1067.62540) Full Text: DOI Euclid