Estimating the First‐ and Second‐Order Parameters of a Heavy‐Tailed Distribution

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A multiple threshold method for fitting the generalized Pareto distribution to rainfall time series (2010, background): “…several authors (e.g., Davison and Smith, 1990; Smith, 1994; Lang et al., 1999; Dupuis, 1998; Choulakian and Stephens, 2001; Guillou and Hall, 2001; Peng and Qi, 2004), but what can be assumed as an optimal threshold for rainfall observations is still an open question without a definitive answer.”
Reduced-Bias Tail Index Estimators Under a Third-Order Framework (2009, background): “Note that Peng and Qi ( 2004 ) derived this same asymptotic variance for an approximate second-order maximum-likelihood tail index estimator.”
Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses (2007, unknown): “1−ρ/4=ρ4 (Feuerverger and Hall, 1999; Peng and Qi, 2004).”
Performances of some parameter estimators of the generalized Pareto distribution over rounded-off samples (2009, background): “…(2001), a paper by Peng and Qi (2004) proposes an alternative approach to the selection of an optimal threshold: rather than searching for the correct threshold, Peng and Qi (2004) look for powerful and robust estimators with moderated bias also for too low (or too high) values of the threshold.”
Second-order refined peaks-over-threshold modelling for heavy-tailed distributions (2009, methodology): “In the same spirit as in this paper, a mixture model with two Pareto components was proposed in Peng and Qi (2004).”