On rank estimation in symmetric matrices: the case of indefinite matrix estimators
AbstractWe focus on the problem of rank estimation in 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 also 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 eigenvalues of the matrix estimator. We discuss several applications where rank estimation in symmetric matrices is of interest, and also provide a small simulation study and an application.
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Bibliographic InfoPaper provided by Universidade do Porto, Faculdade de Economia do Porto in its series FEP Working Papers with number 167.
Length: 27 pages.
Date of creation: Feb 2005
Date of revision:
rank; symmetric matrix; eigenvalues; matrix decompositions; estimation; asymptotic normality; consistency;
Other versions of this item:
- Donald, Stephen G. & Fortuna, Nat rcia & Pipiras, Vladas, 2007. "On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 23(06), pages 1217-1232, December.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-02-20 (All new papers)
- NEP-ECM-2005-02-23 (Econometrics)
- NEP-ETS-2005-03-09 (Econometric Time Series)
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