Annals of Operations Research

, Volume 181, Issue 1, pp 377–392 | Cite as

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

  • Kristof De Witte
  • Rui C. Marques
Open Access


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.


Nonparametric estimation Frontier Non-oriented Outliers Water sector 


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Centre for Economic StudiesUniversity of Leuven (KU Leuven)LeuvenBelgium
  2. 2.Top Institute for Evidence Based Education ResearchMaastricht UniversityMaastrichtThe Netherlands
  3. 3.Centre of Urban and Regional SystemsTechnical University of LisbonLisbonPortugal

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