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}
}
View PDF on arXiv
41 Citations
Highly Influential Citations
3
Background Citations
15
Methods Citations
14
Results Citations
1

Figures and Tables from this paper

41 Citations

Non-Linear Models for Extremal Dependence
TLDR
A flexible, semi-parametric method for the estimation of non-stationary multivariate Pickands dependence functions, based on an accurate max-projection, that performs well and is competitive with the standard estimators in the absence of covariates.
Non-parametric estimator of a multivariate madogram for missing-data and extreme value framework
The modeling of dependence between maxima is an important subject in several applications in risk analysis. To this aim, the extreme value copula function, characterised via the madogram, can be used…
Nonparametric estimation of the dependence among multivariate rainfall maxima
Multivariate analysis of extreme values has an increasing range of applications in risk analysis, especially in the fields of environmental sciences. For example, it would be of interest for…
Bayesian Inference for the Extremal Dependence
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the…
A semi‐parametric stochastic generator for bivariate extreme events
The analysis of multiple extreme values aims to describe the stochastic behaviour of observations in the joint upper tail of a distribution function. For instance, being able to simulate multivariate…
Statistical modelling and inference for covariate-dependent extremal dependence
TLDR
These proposals for the flexible incorporation of covariate influence rely on the (vector) generalized additive modelling infrastructure, and are established in a parametric setting and a non-parametric setting where they develop projection techniques enabling the reduction of the problem of characterizing joint tail dependences to the modelling of univariate random variables.
A comparison of dependence function estimators in multivariate extremes
TLDR
This paper investigates the performance of nonparametric methods and then compares them with classical parametric approaches under symmetric and asymmetric dependence structures within the commonly used logistic family and explores two different ways to makeNonparametric estimators satisfy the necessary dependence function shape constraints.
Modelling non-stationarity in asymptotically independent extremes
TLDR
A novel semi-parametric modelling framework for bivariate extremal dependence structures is proposed that is able to capture observed dependence trends and, in combination with models for marginal non-stationarity, can be used to produce estimates of bivariate risk measures at future time points.
Multivariate extremes over a random number of observations
The classical multivariate extreme‐value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max‐stable distributions. In this work, the classical theory…
Inference for asymptotically independent samples of extremes
...
...

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…
Nonparametric estimation of the dependence function for a multivariate extreme value distribution
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…
...
...