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How to improve the performances of DEA/FDH estimators in the presence of noise?

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Abstract

In frontier analysis, most nonparametric approaches (DEA, FDH) are based on envelopment ideas which assume that with probability one, all observed units belong to the attainable set. In these “deterministic” frontier models, statistical inference is now possible, by using bootstrap procedures. In the presence of noise, envelopment estimators could behave dramatically since they are very sensitive to extreme observations that might result only from noise. DEA/FDH techniques would provide estimators with an error of the order of the standard deviation of the noise. This paper adapts some recent results on detecting change points [Hall P, Simar L (2002) J Am Stat Assoc 97:523–534] to improve the performances of the classical DEA/FDH estimators in the presence of noise. We show by simulated examples that the procedure works well, and better than the standard DEA/FDH estimators, when the noise is of moderate size in term of signal to noise ratio. It turns out that the procedure is also robust to outliers. The paper can be seen as a first attempt to formalize stochastic DEA/FDH estimators.

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Acknowledgements

Research support from “Projet d’Actions de Recherche Concertées” (No. 98/03–217) and from the “Interuniversity Attraction Pole”, Phase V (P5/24) and Phase VI (P6/03) from the Belgian Government (Belgian Science Policy) are acknowledged. Constructive comments of two anonymous referees and of the Associate Editor on previous versions of the paper are also acknowledged.

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  1. Institut de Statistique, Université Catholique de Louvain, 20, voie du Roman Pays, 1438, Louvain-la-Neuve, Belgium

    Léopold Simar

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Correspondence to Léopold Simar.

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Simar, L. How to improve the performances of DEA/FDH estimators in the presence of noise?. J Prod Anal 28, 183–201 (2007). https://doi.org/10.1007/s11123-007-0057-3

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