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Discriminant analysis of distributional data via fractional programming

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  • Dias, Sónia
  • Brito, Paula
  • Amaral, Paula

Abstract

We address classification of distributional data, where units are described by histogram or interval-valued variables. The proposed approach uses a linear discriminant function where distributions or intervals are represented by quantile functions, under specific assumptions. This discriminant function allows defining a score for each unit, in the form of a quantile function, which is used to classify the units in two a priori groups, using the Mallows distance. There is a diversity of application areas for the proposed linear discriminant method. In this work we classify the airline companies operating in NY airports based on air time and arrival/departure delays, using a full year flights.

Suggested Citation

  • Dias, Sónia & Brito, Paula & Amaral, Paula, 2021. "Discriminant analysis of distributional data via fractional programming," European Journal of Operational Research, Elsevier, vol. 294(1), pages 206-218.
    • Handle: RePEc:eee:ejores:v:294:y:2021:i:1:p:206-218
    DOI: 10.1016/j.ejor.2021.01.025
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    References listed on IDEAS

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    1. Antonio Irpino & Rosanna Verde, 2015. "Basic statistics for distributional symbolic variables: a new metric-based approach," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(2), pages 143-175, June.
    2. Billard L. & Diday E., 2003. "From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 470-487, January.
    3. A. Silva & Paula Brito, 2015. "Discriminant Analysis of Interval Data: An Assessment of Parametric and Distance-Based Approaches," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 516-541, October.
    4. António Silva & Paula Brito, 2006. "Linear discriminant analysis for interval data," Computational Statistics, Springer, vol. 21(2), pages 289-308, June.
    5. Gloria Gonzalez-Rivera & Javier Arroyo & Carlos Mate & A. Munoz San Roque, 2011. "Smoothing Methods for Histogram-valued Time Series. An Application to Value-at-Risk," Working Papers 201433, University of California at Riverside, Department of Economics.
    6. Arroyo, Javier & Maté, Carlos, 2009. "Forecasting histogram time series with k-nearest neighbours methods," International Journal of Forecasting, Elsevier, vol. 25(1), pages 192-207.
    7. González-Rivera, Gloria & Arroyo, Javier, 2012. "Time series modeling of histogram-valued data: The daily histogram time series of S&P500 intradaily returns," International Journal of Forecasting, Elsevier, vol. 28(1), pages 20-33.
    8. Dias, Sónia & Brito, Paula, 2017. "Off the beaten track: A new linear model for interval data," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1118-1130.
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    Cited by:

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    2. Jiao, Hongwei & Li, Binbin, 2022. "Solving min–max linear fractional programs based on image space branch-and-bound scheme," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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