A new class of estimators of a “scale” second order parameter

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A simple second-order reduced bias’ tail index estimator (2007, background): “13 , and may be defined as where with The statistics <inline-graphic xmlns:xlink="http://www.”
Reduced-Bias Tail Index Estimators Under a Third-Order Framework (2009, background): “Such a class of estimators has been first parameterised in a tuning parameter τ > 0, but more generally, τ can be considered as a real number (Caeiro and Gomes, 2006 ).”
Nonparametric regression estimation of conditional tails: the random covariate case (2014, unknown): “[24] and Caeiro and Gomes,[27] we introduce the following class of estimators for ρ(x), parameterized in terms of a tuning parameter τ ∈ R: ρ̂n(x; K, L, τ) := 3(Rn(x; K, L, τ) − 1) Rn(x; K, L, τ) − 3 ,”