Statistical Inferences of Data Envelopment Analysis

10.29973/JCSA.200509.0005

Chieh-Yu Liu

Data Envelopment Analysis DEA ； Hodges-Lehmann procedure ； bootstrap

中國統計學報

43卷3期（2005 / 09 / 01）

337 - 352

英文

Data Envelopment Analysis (DEA) is a mathematical programming method which calculates the input-output efficiency of a decision-making unit (DMU). In tills paper, we tried to solve two problems which could he 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 he 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 he 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 hut also provide statistical information for DEA method.

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