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Limiting behavior of weighted sums of heavy-tailed random vectors and applications

Pingyan C., Scheffler H.-P.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 2

281--295

We present an integral test to determine the limiting behavior of weighted sums of i.i.d. Rd-valued random vectors belonging to the (generalized) domain of operator semistable attraction of some nonnormal law, and deduce a version of Chover’s law of the iterated logarithm for them. As applications, the corresponding limit results for some classical summability methods are also established.