On Exponential Representations of Log-Spacings of Extreme Order Statistics
Authors: Beirlant, J.1; Dierckx, G.2; Guillou, A.3; Staˇricaˇ, C.4
Source: Extremes, Volume 5, Number 2, June 2002 , pp. 157-180(24)
Publisher: Springer
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Abstract:
In Beirlant et al. (1999) and Feuerverger and Hall (1999) an exponential regression model (ERM) was introduced on the basis of scaled log-spacings between subsequent extreme order statistics from a Pareto-type distribution. This lead to the construction of new bias-corrected estimators for the tail index. In this note, under quite general conditions, asymptotic justification for this regression model is given as well as for resulting tail index estimators. Also, we discuss diagnostic methods for adaptive selection of the threshold when using the Hill (1975) estimator which follow from the ERM approach. We show how the diagnostic presented in Guillou and Hall (2001) is linked to the ERM, while a new proposal is suggested. We also provide some small sample comparisons with other existing methods.Keywords: Pareto index; quantile plots; regression; asymptotics
Document Type: Research article
Affiliations: 1: University Center of Statistics, W. de Croylaan 52B, 3001 Heverlee, Belgium jan.beirlant@wis.kuleuven.ac.be 2: Department of Statistics, Potchefstroom University for CHE, Potchefstroom 2520, South Africa sttgmad@puknet.puk.ac.za 3: Université Paris VI, LSTA, Boîte 158, 4 place jussieu, 75252 Paris cedex 05, France guillou@ccr.jussieu.fr 4: Mathematical Statistics, Chalmers University of Technology, S-412 96 Goteborg, Sweden starica@math.chalmers.se
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