Confidence intervals for DEA-type efficiency scores: how to avoid the computational burden of the bootstrap

Badin, Luisa;Simar, Léopold
(2003) , 26 pages

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Abstract
One important issue in statistical inference is to provide confidence intervals for the parameters of interest. Once the statistical properties of the estimators have been established, the corresponding asymptotic results can be used for constructing confidence intervals. However, in nonparametric efficiency estimation, the asymptotic properties of DEA estimators are only available for the bivariate case (Gijbels et al., 1999). An appealing alternative is the bootstrap method and a general methodology for applying bootstrap in nonparametric frontier estimation is provided by Simar and Wilson (1998, 2000b). Nevertheless, all the procedures involving bootstrap method are based on a large number of data replications, and in frontier estimation this approach also implies performing DEA (i.e. solving linear programs) a large number of times. Hence, a more simple and less computing intensive technique is always welcome. In this paper we propose a simple procedure for constructing confidence intervals for the efficiency scores. We consider some classical confidence intervals for an end-point of a distribution and we show how these results can be adapted to the problem of frontier estimation. We provide an algorithm for constructing similar confidence intervals for the efficiency scores. Then some Monte Carlo experiments estimate the coverage probabilities of the obtained intervals. The results are quite satisfactory even for small samples. We then illustrate the approach with a real data set when analyzing the efficiency of 36 Air Controllers in Europe.
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  • Academy of Economic StudiesDepartment of Mathematics

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Badin, L., & Simar, L. (2003). Confidence intervals for DEA-type efficiency scores: how to avoid the computational burden of the bootstrap (STAT Discussion Papers 0316). https://hdl.handle.net/2078.5/33170