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A note on construction of heuristically optimal Pena’s synthetic indicators by the particle swarm method of global optimization

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Abstract

Pena’s method of construction of a synthetic indicator is very sensitive to the order in which the constituent variables (whose linear aggregation yields the synthetic indicator) are arranged. Due to this, Pena’s method can at present give only an arbitrary synthetic indicator whose representativeness is indeterminate and uncertain, especially when the number of constituent variables is not very small. This paper uses discrete global optimization method based on the Particle Swarms to obtain a heuristically optimal order in which the constituent variables can be arranged so as to yield Pena’s synthetic indicator that maximizes the minimal absolute (or squared) correlation with its constituent variables.

Suggested Citation

  • Mishra, SK, 2012. "A note on construction of heuristically optimal Pena’s synthetic indicators by the particle swarm method of global optimization," MPRA Paper 37625, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:37625
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    File URL: https://mpra.ub.uni-muenchen.de/37625/1/MPRA_paper_37625.pdf
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    References listed on IDEAS

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    1. 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.
    2. Mishra, SK, 2007. "A Note on Human Development Indices with Income Equalities," MPRA Paper 3513, University Library of Munich, Germany.
    3. Mishra, SK, 2007. "A Comparative Study of Various Inclusive Indices and the Index Constructed by the Principal Components Analysis," MPRA Paper 3377, University Library of Munich, Germany.
    4. Mishra, SK, 2006. "Performance of Differential Evolution and Particle Swarm Methods on Some Relatively Harder Multi-modal Benchmark Functions," MPRA Paper 449, University Library of Munich, Germany.
    5. José-María Montero & Coro Chasco & Beatriz Larraz, 2010. "Building an environmental quality index for a big city: a spatial interpolation approach combined with a distance indicator," Journal of Geographical Systems, Springer, vol. 12(4), pages 435-459, December.
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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. Mishra, SK, 2012. "A comparative study of trends in globalization using different synthetic indicators," MPRA Paper 38028, University Library of Munich, Germany.
    3. Mishra, SK, 2012. "A maximum entropy perspective of Pena’s synthetic indicators," MPRA Paper 37797, University Library of Munich, Germany.
    4. Mishra, SK, 2012. "Construction of Pena’s DP2-based ordinal synthetic indicator when partial indicators are rank scores," MPRA Paper 39088, University Library of Munich, Germany.
    5. Santanu Ray, 2014. "An Index of Maternal and Child Healthcare Status in India: Measuring Inter- and Intra-State Variations from Capability Perspectives," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 117(1), pages 195-207, May.

    More about this item

    Keywords

    Synthetic indicators; Pena’s distance; Particle swarm; Discrete Global Optimization; Composite indices; Maxi-min absolute correlation;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • 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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