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Products of independent,normally attracted random variables

Authors:	Peter Hall Eugene Seneta

Affiliation:	(1) Department of Statistics, Australian National University, G.P.O. Box 4, 2601 Canberra, ACT, Australia;(2) Department of Mathematical Statistics, University of Sydney, 2006 Sydney, N.S.W., Australia

Abstract:	Summary LetR_n denote the correlation coefficient of ann-sample of pairs (X_i,Y_i), each distributed as (X, Y). AssumeX andY are independent and in the domain of attraction of the Normal law. It is shown that this entailsXY being in that domain of attraction, and thatd_nR_nN(0, 1) in distribution for constantsd_n satisfying lim sup(n^1/2/d_n)1. Examples illustrate details of these limit theorems.

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