Skip to content
Home
About Us
Resources
Profiles Metrics
Authors Directory
Institutions Directory
Top Authors
Top Institutions
Top Sponsors
AI Digest
Contact Us
Menu
Home
About Us
Resources
Profiles Metrics
Authors Directory
Institutions Directory
Top Authors
Top Institutions
Top Sponsors
AI Digest
Contact Us
Home
About Us
Resources
Profiles Metrics
Authors Directory
Institutions Directory
Top Authors
Top Institutions
Top Sponsors
AI Digest
Contact Us
Menu
Home
About Us
Resources
Profiles Metrics
Authors Directory
Institutions Directory
Top Authors
Top Institutions
Top Sponsors
AI Digest
Contact Us
Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
decision sciences
Kernel estimators for the second order parameter in extreme value statistics
Journal of Statistical Planning and Inference, Volume 140, No. 9, Year 2010
Notification
URL copied to clipboard!
Description
We develop and study in the framework of Pareto-type distributions a general class of kernel estimators for the second order parameter ρ, 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 ρ, we construct estimators for ρ 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 ρ 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. © 2010 Elsevier B.V.
Authors & Co-Authors
Goegebeur, Yuri
Denmark, Odense
Syddansk Universitet
Beirlant, Jan
Belgium, Heverlee
Leuven Statistics Research Centre
de Wet, Tertius
South Africa, Stellenbosch
Stellenbosch University
Statistics
Citations: 73
Authors: 3
Affiliations: 3
Identifiers
Doi:
10.1016/j.jspi.2010.03.029
ISSN:
03783758