LINKING PARETO-TAIL KERNEL GOODNESS-OF-FIT STATISTICS WITH TAIL INDEX AT OPTIMAL THRESHOLD AND SECOND ORDER ESTIMATION

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Kernel estimators for the second order parameter in extreme value statistics (2010, methodology): “The approach we follow is based on the kernel goodness-of-fit statistics introduced in Goegebeur et al. (2008).”
Threshold detection for the generalized Pareto distribution: Review of representative methods and application to the NOAA NCDC daily rainfall database (2016, methodology): “0 [see e.g., Goegebeur et al., 2008].”
Automated threshold selection for extreme value analysis via ordered goodness-of-fit tests with adjustment for false discovery rate (2018, methodology): “Langousis et al. (2016) detail a few of these procedures for threshold selection, such as the Jackson [Jackson (1967)] and Lewis [Lewis (1965)] kernel statistics as modified in Goegebeur, Beirlant and de Wet (2008) (based on the Hill estimator) and an automated version of the mean residual life (MRL”
A Review of Extreme Value Threshold Estimation and Uncertainty Quantification (2012, methodology): “Goegebeur et al. (2008) further considered a kernel based goodness of fit statistic of the tail fit in the Pareto type tail case, extending Hill (1975), but taking advantage of the relationship between the specific kernel statistics and bias in the asymptotic mean square error of the Hill estimator.”