THE ASYMPTOTICS OF L-STATISTICS FOR NON I.I.D. VARIABLES WITH
Abstract: The purpose of this paper is to study the asymptotic behaviour of linear combinations
of order statistics (-statistics)
for variables with heavy tails. The order statistics
correspond to a
non i.i.d. triangular array
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
regularly varying function
, a case which has often been treated in the literature.
2000 AMS Mathematics Subject Classification: Primary: 62G32; Secondary: 62G30,
Keywords and phrases: L-statistics, shift-compactness, order statistics, heavy tails,
stable law, non i.i.d. array.