A note on necessary and sufficient conditions for proving that a random symmetric matrix converges to a given limit

Robert L. Strawderman

Statistics & Probability Letters, 1994, vol. 21, issue 5, 367-370

Abstract: We demonstrate that if Bk x kn is a sequence of symmetric matrices that converges in probability to some fixed but unspecified nonsingular symmetric matrix B elementwise, then B = B0 for a specified matrix B0 if and only if both the trace and squared Euclidean norm of DnDTn converge to k, where Dn = B-10 Bn. Examples are given to demonstrate how this result may be used to construct hypothesis tests for the equality of covariance matrices and for model misspecification.

Keywords: Convergence; in; probability; Eigenvalues; Euclidean; norm; Random; matrix; Trace (search for similar items in EconPapers)
Date: 1994
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