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Discriminant Analysis of Interval Data: An Assessment of Parametric and Distance-Based Approaches

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  • A. Silva
  • Paula Brito

Abstract

Building on probabilistic models for interval-valued variables, parametric classification rules, based on Normal or Skew-Normal distributions, are derived for interval data. The performance of such rules is then compared with distancebased methods previously investigated. The results show that Gaussian parametric approaches outperform Skew-Normal parametric and distance-based ones in most conditions analyzed. In particular, with heterocedastic data a quadratic Gaussian rule always performs best. Moreover, restricted cases of the variance-covariance matrix lead to parsimonious rules which for small training samples in heterocedastic problems can outperform unrestricted quadratic rules, even in some cases where the model assumed by these rules is not true. These restrictions take into account the particular nature of interval data, where observations are defined by both MidPoints and Ranges, which may or may not be correlated. Under homocedastic conditions linear Gaussian rules are often the best rules, but distance-based methods may perform better in very specific conditions. Copyright Classification Society of North America 2015

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  • 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.
    • Handle: RePEc:spr:jclass:v:32:y:2015:i:3:p:516-541
    DOI: 10.1007/s00357-015-9189-8
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    References listed on IDEAS

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    2. M. Rosário Oliveira & Margarida Azeitona & António Pacheco & Rui Valadas, 2022. "Association measures for interval variables," 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. 16(3), pages 491-520, September.
    3. A. Pedro Duarte Silva & Peter Filzmoser & Paula Brito, 2018. "Outlier detection in interval data," 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. 12(3), pages 785-822, September.
    4. Boris Beranger & Huan Lin & Scott Sisson, 2023. "New models for symbolic data analysis," 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. 17(3), pages 659-699, September.
    5. Rong Guan & Huiwen Wang & Haitao Zheng, 2020. "Improving accuracy of financial distress prediction by considering volatility: an interval-data-based discriminant model," Computational Statistics, Springer, vol. 35(2), pages 491-514, June.
    6. Pierpaolo D’Urso & Riccardo Massari & Livia De Giovanni & Carmela Cappelli, 2017. "Exponential distance-based fuzzy clustering for interval-valued data," Fuzzy Optimization and Decision Making, Springer, vol. 16(1), pages 51-70, March.

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