A Kernel Bayesian Data Envelopment Analysis Approach for Bias Correction of Efficiencies

This study introduces a kernel Bayesian approach to correct the bias of data envelopment analysis (DEA) efficiency estimates. This approach yields consistent estimates for convex sets. The prior distribution of this Bayesian method is “non-informative” in a relative sense as no distributional assumptions are made, like in theoretical Bayesian approaches, and the parameters of DEA efficiency distributions are not used to obtain bias-corrected estimates, as in alternative computational or hybrid Bayesian techniques for statistical inference to efficiencies. Specifically, various kernel distributions, such as Epanechnikov, Biweight, Triweight, and Gaussian, are tested for the prior distribution. In addition, we deploy least cross validation (LCV), rule of thumb (RoT), and least-squares cross validation (LSCV) as bandwidth selection methodologies for every kernel distribution function. Bias correction draws on the ratio of a posterior truncated normal distribution, with μ and σ the respective kernel values, and the above prior kernel distributions with LCV, RoT, and LSCV as bandwidth selection mechanisms. Using scaled samples of 30, 50, 80, and 100 units, the mean square error (MSE) and mean absolute error (MAE) of this Bayesian approach’s estimates are as low as 6.45 × 10–3 and 6.4 × 10–2, respectively. Based on real-world data, we show that the new Bayesian method performs better than extant computational bias-correction techniques for DEA efficiencies. At the same time, the MSE and MAE decrease gradually as the sample size increases.