Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials

@article{Marcon2014MultivariateNE,
  title={Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials},
  author={G. Marcon and Simone A. Padoan and Philippe Naveau and Pietro Muliere and Johan Segers},
  journal={Journal of Statistical Planning and Inference},
  year={2014},
  volume={183},
  pages={1-17}
}

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References

SHOWING 1-10 OF 45 REFERENCES
Nonparametric estimation of multivariate extreme-value copulas
Nonparametric estimation of an extreme-value copula in arbitrary dimensions
A nonparametric estimation procedure for bivariate extreme value copulas
SUMMARY A bivariate extreme value distribution with fixed marginals is generated by a onedimensional map called a dependence function. This paper proposes a new nonparametric estimator of this
New estimators of the Pickands dependence function and a test for extreme-value dependence
We propose a new class of estimators for Pickands dependence function which is based on the best L 2 -approximation of the logarithm of the copula by logarithms of extremevalue copulas. An explicit
Minimum distance estimators of the Pickands dependence function and related tests of multivariate extreme-value dependence
We consider the problem of estimating the Pickands dependence function corresponding to a multivariate extreme-value distribution. A minimum distance estimator is proposed which is based on an
Distribution and dependence-function estimation for bivariate extreme-value distributions
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
Shape restricted nonparametric regression with Bernstein polynomials
RANK-BASED INFERENCE FOR BIVARIATE EXTREME-VALUE COPULAS
Consider a continuous random pair (X, Y ) whose dependence is characterized by an extreme-value copula with Pickands dependence function A. When the marginal distributions of X and Y are known,
Projection estimators of Pickands dependence functions
The authors consider the construction of intrinsic estimators for the Pickands dependence function of an extreme‐value copula. They show how an arbitrary initial estimator can be modified to satisfy
...
...