Statistical Analysis in the DEA Context

Abstract

This paper deals with Data Envelopment Analysis (DEA), where we have several organizational units or Decision Making Units -- DMUs. Each DMU has multiple inputs and multiple outputs. DEA calculates the relative efficiencies of DMUs via linear programming. Various versions of DEA were developed. Although DEA is a deterministic model, during the last two decades statistical methods are used in three main dimensions: 1. In preparing the input and output data and DMUs, 2. As a stochastic alternative to derive DMUs efficiencies, 3. As a second stage after the efficiencies are derived to test the relationship between the efficiency and various environmental parameters. Our paper explores the use of the various statistical methods in the DEA context covering these three main dimensions. The major statistical methods we present are: comparisons including parametric and non-parametric tests, correlation and regression, analyses of variance, multivariate analyses, and bootstrapping. Examples from the literature, using various statistical methods in the DEA context, will be presented along the above three dimensions.