Asymptotic independence of distributions of normalized order statistics of the underlying probability measure

R. -D. Reiss

Journal of Multivariate Analysis, 1981, vol. 11, issue 3, 386-399

Abstract: Let n denote the sample size, and let ri [set membership, variant] {1,...,n} fulfill the conditions ri - ri-1 >= 5 for i = 1,...,k. It is proved that the joint normalized distribution of the order statistics Zri:n, i = 1,...,k, is independent of the underlying probability measure up to a remainder term of order O((k/n)1/2). A counterexample shows that, as far as central order statistics are concerned, this remainder term is not of the order O((k/n)1/2) if ri - ri-1 = 1 for i = 2,...,k.

Keywords: Normalized; order; statistics; uniform; distance; of; measures; over; all; Borel; sets (search for similar items in EconPapers)
Date: 1981
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