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Convergence results for sequences of quadratic forms
Author(s) -
Wilmesmeier James M.,
Wright F. T.
Publication year - 1982
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315074
Subject(s) - mathematics , rate of convergence , sequence (biology) , convergence (economics) , quadratic equation , proofs of convergence of random variables , combinatorics , random variable , convergence tests , convergence of random variables , statistics , sum of normally distributed random variables , computer science , geometry , channel (broadcasting) , economics , economic growth , computer network , genetics , biology
Let (XI,)be a sequence of independent random variables, and let Q n = 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 {Q n } 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.