An inequality for a sum of quadratic forms with applications to probability theory
- Anderson, T.W.
- Taylor, John B.
Publication date
April 1980
DOI Publisher
Published by Elsevier Inc. ISSN
0024-3795 Citation count (estimate)
6Abstract
AbstractLet {xt} be a sequence of p-component vectors, and let At=∑Ts=1xtx′t with An nonsingular for some n⩾p. It is shown that ∑tt=q+1x′tA-2txt⩽trA-1q for n⩽q<T. An application of this proposition is the convergence of a certain martingale with probability 1. A matrix version of Kronecker's lemma then leads to strong consistency of least-squares estimates under a certain condition
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