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Using the bootstrap method to detect influential DMUs in data envelopment analysis

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  • Zijiang Yang
  • Xiaogang Wang
  • Dongming Sun

Abstract

This paper proposes a statistical approach to handle the problem of detecting influential observations in deterministic nonparametric Data Envelopment Analysis (DEA) models. We use the bootstrap method to estimate the underlying distribution for efficiency scores in order to avoid making unrealistic assumptions about the true distribution. To measure whether a specific DMU is truly influential, we employ relative entropy to detect the change in the distribution after the DMU in question is removed. A statistical test has been applied to determine the significance level. Two examples from the literature are discussed and comparisons to previous methods are provided. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Zijiang Yang & Xiaogang Wang & Dongming Sun, 2010. "Using the bootstrap method to detect influential DMUs in data envelopment analysis," Annals of Operations Research, Springer, vol. 173(1), pages 89-103, January.
    • Handle: RePEc:spr:annopr:v:173:y:2010:i:1:p:89-103:10.1007/s10479-009-0520-9
    DOI: 10.1007/s10479-009-0520-9
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    References listed on IDEAS

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    1. Léopold Simar & Paul Wilson, 2000. "Statistical Inference in Nonparametric Frontier Models: The State of the Art," Journal of Productivity Analysis, Springer, vol. 13(1), pages 49-78, January.
    2. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    3. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    4. Pastor, Jesus T. & Ruiz, Jose L. & Sirvent, Inmaculada, 1999. "A statistical test for detecting influential observations in DEA," European Journal of Operational Research, Elsevier, vol. 115(3), pages 542-554, June.
    5. Seaver, Bill L & Triantis, Konstantinos P, 1989. "The Implications of Using Messy Data to Estimate Production-Frontier-Based Technical Efficiency Measures," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 49-59, January.
    6. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
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    8. Wilson, Paul W, 1993. "Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Outputs," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 319-323, July.
    9. A. Charnes & W. W. Cooper & E. Rhodes, 1981. "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through," Management Science, INFORMS, vol. 27(6), pages 668-697, June.
    10. Zhu, Joe, 2001. "Super-efficiency and DEA sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 129(2), pages 443-455, March.
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    Cited by:

    1. Marcel Clermont & Julia Schaefer, 2019. "Identification of Outliers in Data Envelopment Analysis," Schmalenbach Business Review, Springer;Schmalenbach-Gesellschaft, vol. 71(4), pages 475-496, October.
    2. Dana PANCUROVA & Stefan LYOCSA, 2013. "Determinants of Commercial Banks’ Efficiency: Evidence from 11 CEE Countries," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(2), pages 152-179, May.
    3. Ali Bahari & Ali Emrouznejad, 2014. "Influential DMUs and outlier detection in data envelopment analysis with an application to health care," Annals of Operations Research, Springer, vol. 223(1), pages 95-108, December.
    4. S Blancard & J-P Boussemart & H Leleu, 2011. "Measuring potential gains from specialization under non-convex technologies," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1871-1880, October.
    5. Yang, Wei & Shi, Jinfeng & Qiao, Han & Shao, Yanmin & Wang, Shouyang, 2017. "Regional technical efficiency of Chinese Iron and steel industry based on bootstrap network data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 57(C), pages 14-24.

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