Bias reduction and explicit semi-parametric estimation of the tail index

By M. Ivette Gomes, M. J. Martins. 2004

51 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/db293b3f3f16bf8a8894d265646591279a4a85cb

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Citations in the corpus

Reduced-Bias Tail Index Estimators Under a Third-Order Framework (2009, background): “…initiated in Gomes and Martins (2002) on the advantages of using an external estimation of the second order parameter , or even its misspecification as in Gomes and Martins (2004), versus an internal estimation at the same k, which leads to high volatile sample paths for small up to “moderate” k.”
Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses (2007, unknown): “Let us write β̂.k;ρ/=: ( k n )ρ ϕ.ρ/ η.ρ/ = γβ A.n=k/ ϕ.ρ/ η.ρ/ : Following the same reasoning as in Gomes and Martins (2002, 2004), but now under the third-order framework in expression (2.4), we derive for Dk.α/ in expression (3.5) Dk.α/ d= γ α+1 + γZ̄.α+1/k√{.2α+1/k} + A.n=k/ α−ρ+1 { 1+Op ( 1…”
DIRECT REDUCTION OF BIAS OF THE CLASSI- CAL HILL ESTIMATOR ⁄ (2005, background): “Such a decision is related to the discussion in Gomes and Martins (2002) on the advantages of an external estimation of the second order parameter ρ (or even their misspecification, as in Gomes and Martins (2004)) versus an internal estimation at the same level k.”
Second-order refined peaks-over-threshold modelling for heavy-tailed distributions (2009, methodology): “Bias-reduction methods have already been proposed in, amongst others, Feuerverger and Hall (1999), Gomes et al. (2000), Beirlant et al. (1999), Beirlant et al. (2002a), Gomes and Martins (2002), and Gomes and Martins (2004) .”
Improved reduced-bias tail index and quantile estimators (2008, methodology): “From Gomes and Martins (2004), we know that if second order condition U ∈ Rργ and k is a intermediate sequence, then Dα,k d= γ 1− α + γ√ (1− 2α) k Z (α) k + A(n/k) 1− α− ρ ( 1 + op(1) ) , (3.5) for any α ≤ 0, where Z(α)k is asymptotically standard normal.”