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

Constantinos Zacharias (), Panagiotis Zervopoulos, Ali Emrouznejad (), Konstantinos Triantis () and Gang Cheng ()
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Constantinos Zacharias: EY, Financial Services & Risk Management
Ali Emrouznejad: University of Surrey
Konstantinos Triantis: Virginia Tech
Gang Cheng: Peking University

Chapter Chapter 15 in Business Analytics and Decision Making in Practice, 2024, pp 175-185 from Springer

Abstract: Abstract 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.

Keywords: Data envelopment analysis; Bayesian methods; Kernel estimation; Bias correction; Statistical inference (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/978-3-031-61589-4_15

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