Inferência estatística dos estimadores de eficiência obtidos com a técnica fronteira n？o paramétrica de DEA: Uma metodologia de Bootstrap

the efficiency measurement of decision making units is a key-task in contemporary societies. despite the existence of several methodologies with this aim none of them is clearly superior. one of the most used is the non-parametric technique of data envelopment analysis (dea). the dea method has many advantages, therefore, being very popular and widely adopted. however, it doesn？t allow for the results statistical inference, which can constrain its use. this document provides some insights for that debate, discussing and applying the dea technique to 70 water services in portugal. later, a re-sampling (bootstrap) methodology is applied to the results attained by dea, enabling its statistical inference. the quality of the values obtained by the bootstrap depends much on the average efficiency level and on its dispersion. that is, if the average inefficiency gap and its dispersion are considerable, the results will be far from the ones wished. nevertheless, under the opposite circumstances, the results are interesting and satisfactory, surpassing the traditional drawbacks pointed at dea.