Quantile DEA: Estimating qDEA-alpha Efficiency Estimates with Conventional Linear Programming

Conventional non-parametric linear programming (LP) based data envelopment analysis (DEA) models have the advantage of being able to estimate multiple input-output efficiency metrics but suffer from sensitivity to outliers and statistical observational noise. Previous observation-deleting approaches to the outlier/noise problem have been somewhat ad hoc usually requiring iterative LP and non-LP problem solving methods. We present the theory and methodology of quantile-DEA (qDEA), similar in concept to quantile-regression, which enables the analyst to directly use LP to obtain efficiency metrics while specifying that no more than ψ-percent of data points can lie external to the efficiency hull. Estimated qDEA-α frontiers encompassing proportion α = 1 − ψ of the data observations are contrasted to order-α frontier estimates. Quantile DEA is shown to be useful in addressing outliers in a study examining changes in relative state level agricultural efficiency measures over time.