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

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  • Strawderman, Robert L.

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.

Suggested Citation

  • Strawderman, Robert L., 1994. "A note on necessary and sufficient conditions for proving that a random symmetric matrix converges to a given limit," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 367-370, December.
    • Handle: RePEc:eee:stapro:v:21:y:1994:i:5:p:367-370
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    Cited by:

    1. Jin Seo Cho & Halbert White, 2014. "Testing the Equality of Two Positive-Definite Matrices with Application to Information Matrix Testing," Working papers 2014rwp-67, Yonsei University, Yonsei Economics Research Institute.

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