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

Mishra, SK (2008): A note on the sub-optimality of rank ordering of objects on the basis of the leading principal component factor scores.

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).

• Item Type: MPRA Paper
• Language: English
• Keywords: Rankings; sub-optimal; optimality; principal component; factor scores; Differential Evolution; global optimization
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C87 - Econometric Software; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

Kendall, M.G. and Stuart, A. (1968): The Advanced Theory of Statistics, vol. 3, Charles Griffin & Co. London.

Mishra, S.K. (2006) “Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions”, SSRN: http://ssrn.com/abstract=933827

Wikipedia (2008) “Ranking” at Wikipedia, http://en.wikipedia.org/wiki/Rank_order