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Non-parametric estimation of data dimensionality prior to data compression: the case of the human development index

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  • David Canning
  • Declan French
  • Michael Moore

Abstract

In many applications in applied statistics, researchers reduce the complexity of a data set by combining a group of variables into a single measure using a factor analysis or an index number. We argue that such compression loses information if the data actually have high dimensionality. We advocate the use of a non-parametric estimator, commonly used in physics (the Takens estimator ), to estimate the correlation dimension of the data prior to compression. The advantage of this approach over traditional linear data compression approaches is that the data do not have to be linearised. Applying our ideas to the United Nations Human Development Index, we find that the four variables that are used in its construction have dimension 3 and the index loses information.

Suggested Citation

  • David Canning & Declan French & Michael Moore, 2013. "Non-parametric estimation of data dimensionality prior to data compression: the case of the human development index," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 1853-1863, September.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:9:p:1853-1863
    DOI: 10.1080/02664763.2013.798629
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    References listed on IDEAS

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    1. Milorad Kovacevic, 2010. "Review of HDI Critiques and Potential Improvements," Human Development Research Papers (2009 to present) HDRP-2010-33, Human Development Report Office (HDRO), United Nations Development Programme (UNDP).
    2. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
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    1. Panagiotis Ravanos & Giannis Karagiannis, 2023. "Correction: A VEA Benefit-of-the-Doubt Model for the HDI," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 170(2), pages 793-796, November.
    2. Panagiotis Ravanos & Giannis Karagiannis, 2021. "Using VEA to assess effectiveness in the development of human capabilities," Economic Change and Restructuring, Springer, vol. 54(1), pages 75-99, February.
    3. Carlotta Montorsi & Chiara Gigliarano, 2024. "Spatial Comprehensive Well-Being Composite Indicators Based on Bayesian Latent Factor Model: Evidence from Italian Provinces," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 175(2), pages 347-383, November.

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