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Testing the Statistical Significance of Linear Programming Estimators

Author

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  • Dan Horsky

    (William E. Simon Graduate School of Business Administration, University of Rochester, P.O. Box 270100, Rochester, New York 14627)

  • Paul Nelson

    (William E. Simon Graduate School of Business Administration, University of Rochester, P.O. Box 270100, Rochester, New York 14627)

Abstract

Linear programming-based estimation procedures are used in a variety of arenas. Two notable areas are multiattribute utility models (LINMAP) and production frontiers (data envelopment analysis (DEA)). Both LINMAP and DEA have theoretical and managerial advantages. For example, LINMAP treats ordinal-scaled preference data as such in uncovering individual-level attribute weights, while regression treats these preferences as interval scaled. DEA produces easy-to-understand efficiency measures, which allow for improved productivity benchmarking. However, acceptance of these techniques is hindered by the lack of statistical significance tests for their parameter estimates. In this paper, we propose and evaluate such parameter significance tests. Two types of tests are forwarded. The first examines whether a model's fit is significantly reduced when an explanatory variable is deleted. The second is based on generating a standard deviation or distribution for the parameter estimate using nonparametric jackknife or bootstrap techniques. We demonstrate through simulations that both types of tests reliably identify both significant and insignificant parameters. The availability of these tests, especially the relatively simple and easy-to-use tests of the first type, should enhance the utilization of linear programming-based estimation.

Suggested Citation

  • Dan Horsky & Paul Nelson, 2006. "Testing the Statistical Significance of Linear Programming Estimators," Management Science, INFORMS, vol. 52(1), pages 128-135, January.
    • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:1:p:128-135
    DOI: 10.1287/mnsc.1050.0444
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    References listed on IDEAS

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    1. Franklin Dexter & Liam O’Neill & Lei Xin & Johannes Ledolter, 2008. "Sensitivity of super-efficient data envelopment analysis results to individual decision-making units: an example of surgical workload by specialty," Health Care Management Science, Springer, vol. 11(4), pages 307-318, December.
    2. Jun B. Kim & Paulo Albuquerque & Bart J. Bronnenberg, 2010. "Online Demand Under Limited Consumer Search," Marketing Science, INFORMS, vol. 29(6), pages 1001-1023, 11-12.
    3. Jessica Rubiano-Moreno & Samuel Nucamendi-Guillén & Alvaro Cordero-Franco & Alejandro Rodríguez-Magaña, 2022. "An improved LINMAP for multicriteria decision: designing customized incentive portfolios in an organization," Operational Research, Springer, vol. 22(4), pages 3489-3520, September.
    4. N. Avkiran, 2010. "Sensitivity analysis of network DEA illustrated in branch banking," CEPA Working Papers Series WP122010, School of Economics, University of Queensland, Australia.

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