Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series A, Pt. 2, pp. 186--201

EXTREME SUMS OF STRICTLY STATIONARY SEQUENCES OF M-DEPENDENT VARIABLES

By

 T. FLAK and W. SCHMID, University of Ulm

SUMMARY.  Let {Xt} be a strictly stationary sequence of m-dependent random variables on $(\mho, \sum, P)$ with X1~F. In this paper the asymptotic distribution of the sum of the largest sn order statistics of X1, ... , Xn is calculated under the assumption that $s_n \rightarrow \infty$ and $s_n/n \rightarrow 0$ if $n \rightarrow \infty$.

AMS (1980) subject classification.  60G70, 60F05.

Key words and phrases. Order statistics, extreme sums, asymptotic normality, m-dependence, stationarity, extreme value theory.

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