Bernoulli

  • Bernoulli
  • Volume 6, Number 5 (2000), 835-844.

Distribution and dependence-function estimation for bivariate extreme-value distributions

Peter Hall and Nader Tajvidi

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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.

Article information

Source
Bernoulli, Volume 6, Number 5 (2000), 835-844.

Dates
First available in Project Euclid: 6 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081282691

Mathematical Reviews number (MathSciNet)
MR2001h:62066

Zentralblatt MATH identifier
1067.62540

Keywords
convex hull cross-validation marginal distribution multivariate extreme-value distribution nonparametric curve estimation smoothing parameter spline

Citation

Hall, Peter; Tajvidi, Nader. Distribution and dependence-function estimation for bivariate extreme-value distributions. Bernoulli 6 (2000), no. 5, 835--844. https://projecteuclid.org/euclid.bj/1081282691


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