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. |