Nonparametric estimation of the lower tail dependence λ L in bivariate copulas

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Measuring systemic risk in the European banking sector: a copula CoVaR approach (2017, methodology): “…in the tails in the computation of systemic risk metrics, we compute non-parametric (N-P) estimates (average of non-parametric estimates in Dobrić and Schmid (2005)) for upper (λU ) and lower (λL) tail dependence coefficients and sample Kendall’s τ correlation coefficients for each…”
Copula-Based Measures of Multivariate Association (2010, methodology): “λL,n,k have been investigated by several authors using techniques from extreme value theory; we mention Huang [52], Ledford and Tawn [70], Dobri´ c and Schmid [ 20 ], Frahm et al. [31], and Schmidt and Stadtmuller [98].”
Non‐parametric Estimation of Tail Dependence (2006, methodology): “Further nonparametric estimators for the lower tail-dependence coefficient are provided in Dobrić and Schmid (2002). In Section 9, a simulation study compares all introduced nonparametric estimators for the tail-dependence coefficient regarding their finite sample properties.”
Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets (2009, background): “As shown by Dobrić and Schmidt (2005), each of these are consistent estimators for λL provided k, the number of observations in the lower tail, is chosen so that k ≈ √n.”