Title: Kernel estimators for the second order parameter in extreme value statistics
Authors: Goegebeur, Yuri ×
Beirlant, Jan
de Wet, Tertius #
Issue Date: Sep-2010
Publisher: Elsevier
Series Title: Journal of Statistical Planning and Inference vol:140 issue:9 pages:2632-2652
Abstract: We develop and study in the framework of Pareto-type distributions a general class of kernel estimators for the second order parameter rho, a parameter related to the rate of convergence of a sequence of linearly normalized maximum values towards its limit. Inspired by the kernel goodness-of-fit statistics introduced in Goegebeur et al. (2008), for which the mean of the normal limiting distribution is a function of rho, we construct estimators for rho using ratios of ratios of differences of such goodness-of-fit statistics, involving different kernel functions as well as power transformations. The consistency of this class of rho estimators is established under some mild regularity conditions on the kernel function, a second order condition on the tail function 1 - F of the underlying model, and for suitably chosen intermediate order statistics. Asymptotic normality is achieved under a further condition on the tail function, the so-called third order condition. Two specific examples of kernel statistics are studied in greater depth, and their asymptotic behavior illustrated numerically. The finite sample properties are examined by means of a simulation study. (C) 2010 Elsevier B.V. All rights reserved.
ISSN: 0378-3758
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Non-KU Leuven Association publications
× corresponding author
# (joint) last author

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