ON RANK ESTIMATION IN SYMMETRIC MATRICES: THE CASE OF INDEFINITE MATRIX ESTIMATORS

Stephen G. Donald, Natércia Fortuna and Vladas Pipiras

Econometric Theory, 2007, vol. 23, issue 06, pages 1217-1232

Abstract: In this paper we consider estimating the rank of an unknown symmetric matrix based on a symmetric, asymptotically normal estimator of the matrix. The related positive definite limit covariance matrix is assumed to be estimated consistently and to have either a Kronecker product or an arbitrary structure. These assumptions are standard although they exclude the case when the matrix estimator is positive or negative semidefinite. We adapt and reexamine here some available rank tests and introduce a new rank test based on the sum of eigenvalues of the matrix estimator. We discuss two applications where rank estimation in symmetric matrices is of interest, and we also provide a small simulation study.The first author acknowledges the support of an Alfred P. Sloan Foundation Research Fellowship and NSF Grant SES-0196372. We thank the co-editor and the two referees for useful comments and suggestions. CEMPRE Centro de Estudos Macroecon micos e Previs o is supported by the Funda o para a Ci ncia e a Tecnologia, Portugal, through the Programa Operacional Ci ncia, Tecnologia e Inova o (POCTI) of the Quadro Comunit rio de Apoio III, which is financed by FEDER and Portuguese funds.

Date: 2007

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Related works:
Working Paper: On rank estimation in symmetric matrices: the case of indefinite matrix estimators (2005)
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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:23:y:2007:i:06:p:1217-1232_07

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