**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 {X_{t}} be a strictly stationary sequence of m-dependent random variables on $(\mho, \sum, P)$ with X_{1}~F. In this paper the asymptotic distribution of the sum of the largest s_{n} order statistics of X_{1}, ... , X_{n} 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.