ASYMPTOTIC BEHAVIOR OF L-STATISTICS FOR A LARGE CLASS OF TIME SERIES

MADAN L. PURI^{1} AND FRITS H. RUYMGAART^{2}

1Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A. 2Department of Mathematics, Texas Tech University, Lubbock, TX 79409-1042, U.S.A.

(Received December 5, 1991; revised November 12, 1992)

Abstract. In this paper we derive the asymptotic normality of L-statistics with unbounded scores for a large class of time series. To handle the dependence structure, we use the concept of m(n)-decomposability as an alternative to classical mixing concepts.

Key words and phrases: Decomposable processes, mixing, empirical processes for decomposable samples, L-statistics.