Bias-corrected and robust estimation of the bivariate stable tail dependence function

Abstract

We consider the estimation of the bivariate stable tail dependence function and propose a bias-corrected and robust estimator. We establish its asymptotic behavior under suitable assumptions. The finite sample performance of the proposed estimator is examined on a simulation study involving both uncontaminated and contaminated samples.

Local Estimation of the Conditional Stable Tail Dependence Function

“…The empirical estimator of L is then given by The asymptotic behaviour of this estimator was first studied by Huang () (see also Drees & Huang, , de Haan & Ferreira, and Bücher et al , ). We also refer to Peng (), Fougères et al (), Beirlant et al () and Escobar‐Bach et al () where alternative estimators for L were introduced. In the present paper, we extend the empirical estimator to the situation where we observe a random covariate X together with the variables of main interest ( Y (1) ,…, Y ( d ) ).…”

How Sensitive are Tail-Related Risk Measures in a Contamination Neighbourhood?

“…In the spirit of (1.4), Ghosh (2017); Vandewalle et al (2007) established robust estimations of extreme value index. We remark that model (1.4) is different from the model mis-specification studied by Blanchet and Murthy (2016); Engelke and Ivanovs (2017); Escobar-Bach et al (2017) concerning the worst VaR and extreme dependence.…”

Robust estimation of the conditional stable tail dependence function

“…In other words, our contribution in this paper is to introduce a robust estimator of the conditional stable tail dependence function. This topic has been only partially considered in the recent literature, e.g., by Escobar-Bach et al (2017, 2018b. See also Gardes and Girard (2015), de Carvalho (2016), Castro and de Carvalho (2017), Castro et al (2018), Mhalla et al (2019), or Escobar-Bach et al (2020) and Goegebeur et al (2020).…”

“…Also, ξpy 1 , y 2 |xq is assumed to be continuous in py 1 , y 2 , xq and homogeneous of order βpxq ą 0 in py 1 , y 2 q. Model (1) was introduced in a simpler context without covariates in Dutang et al (2014) and Escobar-Bach et al (2017), see also Beirlant et al (2011), and it has its roots in Ledford and Tawn (1997). Essentially (1) is a further assumption on the tail copula that underlies the joint distribution of pY p1q , Y p2q q, conditional on X " x.…”

“…Compared to related recent literature on estimation of extremal dependence the differences are as follows. Escobar-Bach et al (2017) consider robust estimation of the stable tail dependence function though in a context without covariates. Escobar-Bach et al (2018a) derive a robust estimator for the Pickands dependence function in a context with covariates, where they assume that the underlying conditional distribution has a conditional extreme value copula.…”