Robust nonparametric estimation of the conditional tail dependence coefficient

Abstract

We consider robust and nonparametric estimation of the coefficient of tail dependence in presence of random covariates. The estimator is obtained by fitting the extended Pareto distribution locally to properly transformed bivariate observations using the minimum density power divergence criterion. We establish convergence in probability and asymptotic normality of the proposed estimator under some regularity conditions. The finite sample performance is evaluated with a small simulation experiment, and the practical applicability of the method is illustrated on a real dataset of air pollution measurements.

Estimation of Copulas via Maximum Mean Discrepancy

“…Denecke and Müller (2011) proposed a parametric robust estimation method based on likelihood depth (Rousseeuw and Hubert 1999). Recently, Goegebeur et al (2020) have considered robust and nonparametric estimation of the coefficient of tail dependence in presence of random covariates, that may be a way of estimating copulas for some particular models. Therefore, even if many estimators have been proposed for Huber contaminated models in general parametric cases, this has not been the case for semiparametric copula models yet.…”

Estimation of copulas via Maximum Mean Discrepancy

“…[14] proposed a parametric robust estimation method based on likelihood depth ( [29]). Recently, [18] have considered robust and nonparametric estimation of the coefficient of tail dependence in presence of random covariates, that may be a way of estimating copulas for some particular models. Therefore, even if many estimators have been proposed for Huber contaminated models in general parametric cases, this has not been the case for semiparametric copula models yet.…”

Robust estimation 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). Concretely, throughout the paper, we denote by pY p1q , Y p2q q a bivariate random vector recorded along with a random covariate X P R d .…”

“…In Escobar-Bach et al (2018b) an estimator for the stable tail dependence function is introduced in a regression context, where it is assumed that the underlying conditional distribution has a dependence function that converges to that of a conditional extreme value distribution, though their estimator is not robust with respect to outlying observations. Goegebeur et al (2020) discuss a robust estimator for the coefficient of tail dependence in the context of random covariates. In some sense, the present paper can be viewed as a follow-up of the latter paper, although the problem considered in Goegebeur et al (2020) is simpler than the one considered in the present paper since now the aim is to estimate a dependence function rather than a single parameter.…”

“…Goegebeur et al (2020) discuss a robust estimator for the coefficient of tail dependence in the context of random covariates. In some sense, the present paper can be viewed as a follow-up of the latter paper, although the problem considered in Goegebeur et al (2020) is simpler than the one considered in the present paper since now the aim is to estimate a dependence function rather than a single parameter. Also, in a deterministic, i.e., non-random, intermediate threshold is used, while in the present paper we consider the more realistic situation where the intermediate threshold is taken as an intermediate conditional quantile, which complicates the asymptotic analysis considerably.…”