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A note on variability of interval data

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Abstract

This paper responds to the following question, namely, when we have interval values for the observations, what is the interval of possible values of their variance. In parallel, we provide a response to the same question when the variance is replaced by the mean of the absolute values of the residuals from the median. Several solutions ranging from the linear and quadratic programming to different search algorithms are discussed.

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References

  • Coleman T, Branch MA, Grace A (1999) Optimization toolbox for use with Matlab. The MathWorks, Natick

    Google Scholar 

  • Computational Statistics (2006) Special Issue on Interval Data, 21(2)

  • Ferson et al. Computing variance for interval data is NP-hard. http://www.cs.utep.edu/vladik/2002/tr02-13b.pdf

  • Gioia F, Lauro NC (2006) Principal component analysis on interval data. Comput Stat 21(2): 243–263

    Article  MathSciNet  Google Scholar 

  • Kreinovich V et al (2006) Towards combining probabilistic and interval uncertainty in engineering calculations: algorithms for computing statistics under interval uncertainty, and their computational complexity. Reliab Comput 12: 471–501

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics, Charles University of Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Jaromír Antoch

  2. Department of Mathematics, Technical University, Hálkova 6, 461 17, Liberec, Czech Republic

    Miroslav Brzezina

  3. Department of Mathematics and Statistics, University Federico II, via Cinthia, 80 126, Napoli, Italy

    Rafaelle Miele

Authors
  1. Jaromír Antoch
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  2. Miroslav Brzezina
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  3. Rafaelle Miele
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Corresponding author

Correspondence to Jaromír Antoch.

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Antoch, J., Brzezina, M. & Miele, R. A note on variability of interval data. Comput Stat 25, 143–153 (2010). https://doi.org/10.1007/s00180-009-0166-8

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  • DOI: https://doi.org/10.1007/s00180-009-0166-8

Keywords

Mathematics Subject Classification (2000)