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On the construction of an aggregated measure of the development of interval data

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  • Andrzej Młodak

Abstract

We analyse some possibilities for constructing an aggregated measure of the development of socio-economical objects in terms of their composite phenomenon (i.e., phenomenon described by many statistical features) if the relevant data are expressed as intervals. Such a measure, based on the deviation of the data structure for a given object from the benchmark of development is a useful tool for ordering, comparing and clustering objects. We present the construction of a composite phenomenon when it is described by interval data and discuss various aspects of stimulation and normalization of the diagnostic features as well as a definition of a benchmark of development (based usually on optimum or expected levels of these features). Our investigation includes the following options for the realization of this purpose: transformation of the interval model into a single–valued version without any significant loss of its statistical properties, standardization of pure intervals as well as definition of the interval “ideal” object. For the determination of a distance between intervals, the Hausdorff formula is applied. The simulation study conducted and the empirical analysis showed that the first two variants are especially useful in practice. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Andrzej Młodak, 2014. "On the construction of an aggregated measure of the development of interval data," Computational Statistics, Springer, vol. 29(5), pages 895-929, October.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:895-929
    DOI: 10.1007/s00180-013-0469-7
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    References listed on IDEAS

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    1. Federica Gioia & Carlo Lauro, 2006. "Principal component analysis on interval data," Computational Statistics, Springer, vol. 21(2), pages 343-363, June.
    2. Adi Ben-Israel & Cem Iyigun, 2008. "Probabilistic D-Clustering," Journal of Classification, Springer;The Classification Society, vol. 25(1), pages 5-26, June.
    3. Marie Chavent & Francisco Carvalho & Yves Lechevallier & Rosanna Verde, 2006. "New clustering methods for interval data," Computational Statistics, Springer, vol. 21(2), pages 211-229, June.
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