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A note on the sub-optimality of rank ordering of objects on the basis of the leading principal component factor scores

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Mishra, SK

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Abstract

This paper demonstrates that if we intend to optimally rank order n objects (candidates) each of which has m attributes or rank scores awarded by m evaluators, then the ordinal ranking of objects by the conventional principal component based factor scores turns out to be suboptimal. Three numerical examples have been provided to show that principal component based rankings do not necessarily maximize the sum of squared correlation coefficients between the individual m rank scores arrays, X(n,m), and overall rank scores array, Z(n).

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File URL: http://mpra.ub.uni-muenchen.de/12419/
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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12419.

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Date of creation: 30 Dec 2008
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Handle: RePEc:pra:mprapa:12419

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Related research
Keywords: Rankings; sub-optimal; optimality; principal component; factor scores; Differential Evolution; global optimization;

Find related papers by JEL classification:
C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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