Faculty Publications

Convergence Results For Sequences Of Quadratic Forms

Document Type

Article

Keywords

degenerate convergence, Quadratic forms, rates of convergence., tail probabilities

Journal/Book/Conference Title

Canadian Journal of Statistics

Volume

10

Issue

1

First Page

39

Last Page

47

Abstract

Let (XI,)be a sequence of independent random variables, and let Qn= where for each N,(an:,k)is a doubly indexed sequence of weights. The convergence and the rate of convergence of the sequence of quadratic forms {Qn} are studied. These quadratic forms are linear sums of dependent variables; however, their convergence properties are similar to those of linear sums of independent variables provided the variables have finite rth absolute moments with 0 < r 2.while the rate of convergence has not been obtained for r< 2, it is shown to be different from that of linear sums. Copyright © 1982 Statistical Society of Canada

Department

Department of Management

Original Publication Date

1-1-1982

DOI of published version

10.2307/3315074

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