MOMENTS OF LIMITS OF LIGHTLY TRIMMED SUMS OF RANDOM VECTORS IN THE GENERALIZED DOMAIN

OF NORMAL ATTRACTION OF NON-GAUSSIAN OPERATOR-STABLE LAWS

MAKOTO MAEJIMA

Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223, Japan

(Received February 28, 1996; revised September 11, 1996)

Abstract. Existence and nonexistence for moments of limiting random vectors of normalized, lightly trimmed sums of random vectors in the generalized domain of normal attraction of non-Gaussian operator-stable laws are studied. The idea of representing the limiting random vectors by infinite series is essentially used in the proofs.

Key words and phrases: Lightly trimmed sum, non-Gaussian operator-stable law, generalized domain of normal attraction, moment, tail behavior.