Influential observations in frontier models, a robust non-oriented approach to the water sector

Kristof De Witte*, Rui C. Marques

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

85 Citations (Web of Science)


This paper suggests an outlier detection procedure which applies a nonparametric model accounting for undesired outputs and exogenous influences in the sample. Although efficiency is estimated in a deterministic frontier approach, each potential outlier initially benefits of the doubt of not being an outlier. We survey several outlier detection procedures and select five complementary methodologies which, taken together, are able to detect all influential observations. To exploit the singularity of the leverage and the peer count, the super-efficiency and the order-m method and the peer index, it is proposed to select these observations as outliers which are simultaneously revealed as atypical by at least two of the procedures. A simulated example demonstrates the usefulness of this approach. The model is applied to the portuguese drinking water sector, for which we have an unusually rich data set.
Original languageEnglish
Pages (from-to)377-392
JournalAnnals of Operations Research
Issue number1
Publication statusPublished - Dec 2010


  • Nonparametric estimation
  • Frontier
  • Non-oriented
  • Outliers
  • Water sector

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