Mishra, SK (2008): On construction of robust composite indices by linear aggregation.
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In this paper we construct thirteen different types of composite indices by linear combination of indicator variables (with and without outliers/data corruption). Weights of different indicator variables are obtained by maximization of the sum of squared (and, alternatively, absolute) correlation coefficients of the composite indices with the constituent indicator variables. Seven different types of correlation are used: Karl Pearson, Spearman, Signum, Bradley, Shevlyakov, Campbell and modified Campbell. Composite indices have also been constructed by maximization of the minimal correlation. We find that performance of indices based on robust measures of correlation such as modified Campbell and Spearman, as well as that of the maxi-min based method, is excellent. Using these methods we obtain composite indices that are autochthonously sensitive and allochthonously robust. This paper also justifies a use of simple mean-based composite indices, often used in construction of human development index.
|Item Type:||MPRA Paper|
|Original Title:||On construction of robust composite indices by linear aggregation|
|Keywords:||Composite index; linear aggregation; principal components; robust correlation; Spearman, Signum; Bradley; Shevlyakov; Campbell; Hampel; outliers; mutilation of data|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General
C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63 - Computational Techniques; Simulation Modeling
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
|Depositing User:||Sudhanshu Kumar Mishra|
|Date Deposited:||19. Jun 2008 07:14|
|Last Modified:||13. Feb 2013 08:58|
• Blomqvist, N. (1950) "On a Measure of Dependence between Two Random Variables", Annals of Mathematical Statistics, 21(4): 593-600. • Campbell, N. A. (1980) “Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation”, Applied Statistics, 29 (3): 231-237 • Devlin, S.J., Gnandesikan, R. and Kettenring, J.R. (1981) “Robust Estimation of Dispersion Matrices and Principal Components”, Journal of the American Statistical Association, 76 (374): 354-362. • Gnanadesikan, R. and Kettenring, J.R. (1972) “Robust Estimates, Residuals and Outlier Detection with Multiresponse Data”, Biomatrics, 28: 81-124. • Hampel, F. R., Ronchetti, E.M., Rousseeuw, P.J. and W. A. Stahel, W.A. (1986) Robust Statistics: The Approach Based on Influence Functions, Wiley, New York. • Hill, M. and Tzamir, Y. (1972) "Multidimensional Evaluation of Regional Plans serving Multiple Objectives", Papers in Regional Science, 29(1): 139-165 • Mishra, S.K. (1984) "Taxonomical Analysis of Regional Development by Outranking Relations on Multiple Principal Components". Hill Geographer, Vol. 3(1): 20-28. • Mishra, S. K. (2007a) "Construction of an Index by Maximization of the Sum of its Absolute Correlation Coefficients with the Constituent Variables", Working Papers Series, SSRN: http://ssrn.com/abstract=989088 • Mishra, S. K. (2007b) "A Comparative Study of Various Inclusive Indices and the Index Constructed By the Principal Components Analysis", Working Papers Series, SSRN: http://ssrn.com/abstract=990831 • Munda, G. and Nardo, M. (2005-a) "Constructing Consistent Composite Indicators: the Issue of Weights", Official Publications of the European Communities, European Communities, Luxembourg, available at http://crell.jrc.ec.europa.eu/Well-being/papers/Munda%20Nardo%20euroreport1.pdf • Munda, G. and Nardo, M. (2005-b) "Non-Compensatory Composite Indicators for Ranking Countries: A Defensible Setting", Official Publications of the European Communities, European Communities, Luxembourg, available at http://crell.jrc.ec.europa.eu/Well-being/papers/Munda%20Nardo%20euroreport2.pdf • Shevlyakov, G.L. (1997) “On Robust Estimation of a Correlation Coefficient”, Journal of Mathematical Sciences, 83(3): 434-438. • Spearman, C. (1904) "The Proof and Measurement of Association between Two Things", American. Journal of Psychology, 15: 88-93. • Van Delft, A. and Nijkamp, P. (1976) “A Multi-objective Decision Model for Regional Development, Environmental Quality Control and Industrial Land Use,” Papers in Regional Science, 36(1): 35–57.