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A note on solution of the nearest correlation matrix problem by von-Neumann matrix divergence

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Mishra, SK

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Abstract

In the extant literature a suggestion has been made to solve the nearest correlation matrix problem by a modified von Neumann approximation. In this paper it has been shown that obtaining the nearest positive semi-definite matrix of a given negative definite correlation matrix by such method is either infeasible or suboptimal. First, if a given matrix is already positive semi-definite, there is no need to obtain any other semi-definite matrix closest to it. When the given matrix is negative definite (Q), then only we seek a positive semi-definite matrix closest to it. Then the proposed procedure fails as we cannot find log(Q). Then, if we replace negative eigenvalues of Q by a zero or near-zero values, we obtain a positive-definite matrix, but it is not nearest to the Q matrix; there are indeed other procedures to obtain better approximation

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7798.

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Date of creation: 16 Mar 2008
Date of revision: 07 Apr 2008
Handle: RePEc:pra:mprapa:7798

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Related research
Keywords: Nearest correlation matrix problem positive semidefinite negative definite von Neumann divergence Bergman divergence

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Find related papers by JEL classification:
C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Statistical Decision Theory; Operations Research
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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  3. Peter Dolton, 2001. "Over education in the graduate labour market: Some evidence from alumni data," CEE Discussion Papers 0009, Centre for the Economics of Education, LSE. [Downloadable!]
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  5. Ablo, Emmanuel & Reinikka, Ritva, 1998. "Do budgets really matter? - evidence from public spending on education and health in Uganda," Policy Research Working Paper Series 1926, The World Bank. [Downloadable!]
  6. Mark Sanders & Bas ter Weel, 2000. "Skill-Biased Technical Change: Theoretical Concepts, Empirical Problems and a Survey of the Evidence," DRUID Working Papers 00-8, DRUID, Copenhagen Business School, Department of Industrial Economics and Strategy/Aalborg University, Department of Business Studies. [Downloadable!]
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  7. Pereira, Pedro Telhado & Martins, Pedro Silva, 2001. "Is there a Return-Risk Link in Education?," IZA Discussion Papers 321, Institute for the Study of Labor (IZA). [Downloadable!]
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