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On construction of robust composite indices by linear aggregation

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Abstract

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.

Suggested Citation

  • Mishra, SK, 2008. "On construction of robust composite indices by linear aggregation," MPRA Paper 9232, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:9232
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    File URL: https://mpra.ub.uni-muenchen.de/9232/1/MPRA_paper_9232.pdf
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    References listed on IDEAS

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    1. Mishra, SK, 1984. "Taxonomical analysis of regional development by outranking relations on multiple principal components," MPRA Paper 8989, University Library of Munich, Germany.
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    Cited by:

    1. Nayak, Purusottam & Mishra, SK, 2012. "Efficiency of Pena’s P2 Distance in Construction of Human Development Indices," MPRA Paper 39022, University Library of Munich, Germany.
    2. Nayak, Purusottam & Mishra, SK, 2014. "A state level analysis of the status of social sector in India," MPRA Paper 58144, University Library of Munich, Germany.
    3. Mishra, SK, 2012. "A note on the indeterminacy and arbitrariness of pena’s method of construction of synthetic indicators," MPRA Paper 37534, University Library of Munich, Germany.
    4. Sudhanshu K. MISHRA, 2016. "BA Note on Construction of a Composite Index by Optimization of Shapley Value Shares of the Constituent Variables," Turkish Economic Review, KSP Journals, vol. 3(3), pages 466-472, September.
    5. Matteo Mazziotta & Adriano Pareto, 2016. "On The Construction Of Composite Indices By Principal Components Analysis," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 70(1), pages 103-109, January-A.
    6. Hussein Sayed & Ramadan Hamed & Mohamed Ramadan & Samaa Hosny, 2015. "Using Meta-goal Programming for a New Human Development Indicator with Distinguishable Country Ranks," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 123(1), pages 1-27, August.

    More about this item

    Keywords

    Composite index; linear aggregation; principal components; robust correlation; Spearman; Signum; Bradley; Shevlyakov; Campbell; Hampel; outliers; mutilation of data;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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