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Testing over-representation of observations in subsets of a DEA technology

Author

Listed:
  • Asmild, Mette
  • Hougaard, Jens Leth
  • Olesen, Ole B.

Abstract

This paper proposes a test for whether data are over-represented in a given production zone, i.e. a subset of a production possibility set which has been estimated using the non-parametric Data Envelopment Analysis (DEA) approach. A binomial test is used that relates the number of observations inside such a zone to a discrete probability weighted relative volume of that zone. A Monte Carlo simulation illustrates the performance of the proposed test statistic and provides good estimation of both facet probabilities and the assumed common inefficiency distribution in a three dimensional input space. Potential applications include tests for whether benchmark units dominate more (or less) observations than expected.

Suggested Citation

  • Asmild, Mette & Hougaard, Jens Leth & Olesen, Ole B., 2013. "Testing over-representation of observations in subsets of a DEA technology," European Journal of Operational Research, Elsevier, vol. 230(1), pages 88-96.
    • Handle: RePEc:eee:ejores:v:230:y:2013:i:1:p:88-96
    DOI: 10.1016/j.ejor.2013.03.038
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    References listed on IDEAS

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    1. Leopold Simar & Paul Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 779-802.
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    3. 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.
    4. 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.
    5. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
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    7. Nam Anh Tran & Gerald Shively & Paul Preckel, 2010. "A new method for detecting outliers in Data Envelopment Analysis," Applied Economics Letters, Taylor & Francis Journals, vol. 17(4), pages 313-316.
    8. Ole Olesen & N. Petersen, 2003. "Identification and Use of Efficient Faces and Facets in DEA," Journal of Productivity Analysis, Springer, vol. 20(3), pages 323-360, November.
    9. J. Hartigan, 1985. "Statistical theory in clustering," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 63-76, December.
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    More about this item

    Keywords

    Data Envelopment Analysis (DEA); Over-representation; Data density; Binomial test; Benchmarks;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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