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Descriptive statistics for interval-valued observations in the presence of rules

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Summary

While symbolic data exist in their own right, contemporary datasets can be too large to analyse using traditional statistical methodologies. Aggregation of these large datasets into sets of more managable size perforce produce datasets whose entries are symbolic data. This paper studies the derivation of basic description statistics, in particular, histograms and mean and variances plus joint histograms for interval-valued datasets when logical dependency rules are present. Algorithms for calculating these histograms are also provided.

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References

  • Bertrand, P. & Goupil, F. (2000), ‘Descriptive statistics for symbolic data’, Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical Information from Complex Data (eds. H.-H. Bock and E. Diday), Berlin, Springer-Verlag, pp 103–124.

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  • Billard, L. & Diday, E. (2003), ‘From the statistics of data to the statistics of knowledge: Symbolic data analysis’, journal of the American Statistical Association 98, pp 470–487.

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  • Bock, H.-H. & Diday, E. (2000), ‘Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical Information from Complex Data’, Berlin, Springer-Verlag.

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Authors and Affiliations

  1. Department of Statistics, University of Georgia, 30602-1952, Athens, GA, USA

    L. Billard

  2. CEREMADE, Universite de Paris, 9 Dauphine, 75775, Paris, Cedex 16, France

    E. Diday

Authors
  1. L. Billard
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  2. E. Diday
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Appendices

Appendix A - Histogram Algorithm

figure alg1

Appendix B - Joint Histogram Algorithm

figure alg2

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Billard, L., Diday, E. Descriptive statistics for interval-valued observations in the presence of rules. Computational Statistics 21, 187–210 (2006). https://doi.org/10.1007/s00180-006-0259-6

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  • DOI: https://doi.org/10.1007/s00180-006-0259-6

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