Reduced-Bias Location-Invariant Extreme Value Index Estimation: a Simulation Study

M. Ivette Gomes (1) , Lígia Henriques-Rodrigues (2) , Cristina Miranda (3)

1 DEIO
2 Instituto Politécnico de Tomar
3 ISCA, Universidade de Aveiro

In this paper, we deal with semi-parametric corrected-bias estimation of a positive extreme value index (EVI). Then, the classical EVI-estimators are the Hill estimators, based on any intermediate number k of top order statistics. But these EVI-estimators are not location-invariant, contrarily to the peaks over random threshold (PORT)-Hill estimators, which depend on an extra tuning parameter q. On the basis of second-order minimum-variance reduced-bias (MVRB) EVI-estimators, we shall here consider PORT-MVRB EVI-estimators, and propose the use of a heuristic algorithm, for the adaptive choice of k and q. Applications in the fields of insurance and finance will be provided.

Mots clés: Physical Sciences

Domaines: Calcul [stat.CO]

M. Ivette Gomes, Lígia Henriques-Rodrigues, Cristina Miranda. Reduced-Bias Location-Invariant Extreme Value Index Estimation: a Simulation Study. Communications in Statistics - Simulation and Computation, 2011, 40 (03), pp.424-447. ⟨10.1080/03610918.2010.543297⟩. ⟨hal-00666675⟩