Statistical Inferences of Data Envelopment Analysis

[[abstract]]Data Envelopment Analysis (DEA) is a mathematical programming method which calculates the input-output efficiency of a decision-making unit (DMU). In this paper, we tried to solve two problems which could be frequently met in DEA applications: (1) according to the classical DEA’s definition, a DMU is called the most input-output efficient when its efficiency estimate attain 1. But when there are more than one DMU’s efficiency estimates attaining 1, they are also called the most input-output efficient, and we can not differentiate them any more. If there were more DMUs whose efficiency estimates equal to 1, in practice, it would be difficult for us to interpret such results; (2) because the efficiency estimates calculated by DEA are a set of scalars, they don’t have any statistical information, such as mean, variance, to help us make statistical inference. The second important question may be also asked: how statistically accurate is the efficiency estimates obtained by DEA? The purpose of this paper is to propose a statistical methodology for DEA, which can not only discriminate the DMUs with DEA efficiency estimates originally equal to 1 but also provide statistical information for DEA meth