How to improve the performances of DEA/FDH estimators in the presence of noise? |
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Authors: | Léopold Simar |
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Institution: | (1) Institut de Statistique, Université Catholique de Louvain, 20, voie du Roman Pays, 1438 Louvain-la-Neuve, Belgium |
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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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Keywords: | Frontier Nonparametric estimation Stochastic DEA/FDH Robustness to outliers |
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