A location-invariant probability weighted moment estimation of the Extreme Value Index

• Published in: International journal of computer mathematics Vol. 93; no. 4; pp. 676 - 695
• Main Authors: Caeiro, Frederico, Gomes, M. Ivette, Henriques-Rodrigues, Lígia
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.04.2016; Taylor & Francis Ltd
• Subjects: adaptive semi-parametric estimation; asymptotic properties; bootstrap methodology; Computer simulation; Construction; Econometrics; Economic models; Estimators; Extreme Value Index; Extreme values; heavy tails; location/scale-invariant estimation; Mathematical analysis; Mathematical models; Monte-Carlo simulation; Parameters; Pareto optimality; Primary: 62G32; Probability; Secondary: 65C05; statistics of extremes
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2014.975217

The peaks over random threshold (PORT) methodology and the Pareto probability weighted moments (PPWM) of the largest observations are used to build a class of location-invariant estimators of the Extreme Value Index (EVI), the primary parameter in statistics of extremes. The asymptotic behaviour of such a class of EVI-estimators, the so-called PORT-PPWM EVI-estimators, is derived, and an alternative class of location-invariant EVI-estimators, the generalized Pareto probability weighted moments (GPPWM) EVI-estimators is considered as an alternative. These two classes of estimators, the PORT-PPWM and the GPPWM, jointly with the classical Hill EVI-estimator and a recent class of minimum-variance reduced-bias estimators are compared for finite samples, through a large-scale Monte-Carlo simulation study. An adaptive choice of the tuning parameters under play is put forward and applied to simulated and real data sets.