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Edgeworth expansions for L-statistics

Alberink B., Pap G., van Zuijlen M. C. A.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 2

277--302

We study the approximation by a short Edgeworth expansion of the distribution function of normalized linear combinations [formula] of order statistics of n independent random variables with common distribution function F. Under the assumptions [formula] for some p1, q1, r1 ∈ R p2, q2, r2, C≥0, к ∈ [0.5/4) with an appropriate balance in these parameters, and under additional moment conditions, the rate of uniform convergence is shown to be of order n -1. Moreover, a special case is considered where the cjn are generated by a sequence of weight functions of a special structure.