Document Server@UHasselt
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Repository of the University of Hasselt containing publications in the fields of statistics, computer science, information strategies and material from the Institute for behavioural sciences.
10.
Asymptotic normality for U-statistics based on trimmed samples - Janssen, Paul; Serfling, Robert; Veraverbeke, Noel
Let Xn1 ? cdots, three dots, centered ? Xnn be an ordered sample of size n. We establish asymptotic normality of U-statistics based on the trimmed sample Xn,[?n]+1? cdots, three dots, centered ? Xn,n ? [?n] where 0, ?<1/2. This theorem and its multi-sample generalization are illustrated by various statistics of importance for robust estimation of location, dispersion, etc. This unifies the flexibility of the class of U-statistics and the classical principle of rejection of outliners.
19.
Asymptotic behaviour of Wiener-Hopf factors of a random walk - Veraverbeke, Noel
For a random walk governed by a general distribution function F on (??, +?), we establish the exponential and subexponential asymptotic behaviour of the corresponding right Wiener-Hopf factor F+. The results apply to classes of distribution functions in recent publications: the subexponential class Image and a related (exponential) class Image?. Given the behaviour of F+, the Wiener-Hopf identity is used, to obtain the behaviour of F. To reverse the argument, we derive a new identity, similar in form to the first one. The results for F+ are then fruitfully applied to give a full description of the tail behaviour of...