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The asymptotics of L-statistics for non i.i.d. variables with heavy tails

Barczyk A., Janssen A., Pauly M.

Probability and Mathematical Statistics

2011

Vol. 31, Fasc. 2

285--299

The purpose of this paper is to study the asymptotic behaviour of linear combinations of order statistics (L-statistics)... [formula] for variables with heavy tails. The order statisticsXi:kn correspond to a non i.i.d. triangular array (Xi,n)1≤i≤kn of infinitesimal and rowwise independent random variables. We give sufficient conditions for the convergence of L-statistics to non-normal limit laws and it is shown that only the extremes contribute to the limit distribution, whereas the middle parts vanish. As an example we consider the case, where the extremal partial sums belong to the domain of attraction of a stable law.We also study L-statistics with scores defined by ci,n := J(i/(n + 1)) with a regularly varying function J, a case which has often been treated in the literature.

Early Pliocene heteropods and pteropods (Mollusca, Gastropoda) from Santa Maria Island (Azores, Portugal) : systematics and biostratigraphic implications

Janssen A., Kroh A., Avila S.

Acta Geologica Polonica

2008

Vol. 58, no. 3

355-369

A holoplanktonic mollusc assemblage from Neogene sediments of the Azorean island Santa Maria is described and analysed to determine the age of the sediments. Sixteen taxa are documented (three heteropods, thirteen pteropods), fourteen of which are new records for the fossil fauna of Santa Maria Island. The composition of the heteropod and pteropod assemblage indicates a Zanclean age, which contrasts with earlier age assignments to the Early, Middle or Late Miocene based on benthic molluscs, but is in good agreement with more recent data based on foraminiferal and geochemical evidence. The pteropod Cavolinia marginata (BRONN, 1862) is re-described based on abundant topotypic material and a neotype is designated. The species Cavolinia vendryesiana (GUPPY, 1873) is considered to be a junior subjective synonym of C. marginata. The temporal range of the pteropod Limacina trochiformis (D.ORBIGNY, 1836) is extended to the Zanclean.