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An expectation conditional maximization algorithm for the skew-normal based stochastic frontier model

Author

Listed:
  • Xiaonan Zhu

    (University of North Alabama)

  • Zheng Wei

    (Texas A &M University - Corpus Christi)

  • Tonghui Wang

    (New Mexico State University)

  • S. T. Boris Choy

    (The University of Sydney)

  • Ziwei Ma

    (University of Tennessee at Chattanooga)

Abstract

In this paper, a feasible expectation-conditional-maximization (ECM) algorithm is developed for finding the maximum likelihood estimates of parameters of the skew-normal based stochastic frontier model. The closed-form formulas for updating parameters in CM-steps are derived. The proposed methodology is illustrated with simulations and a real data example, where we find the new ECM algorithm outperforms the numerical approach adopted in the previous study.

Suggested Citation

  • Xiaonan Zhu & Zheng Wei & Tonghui Wang & S. T. Boris Choy & Ziwei Ma, 2024. "An expectation conditional maximization algorithm for the skew-normal based stochastic frontier model," Computational Statistics, Springer, vol. 39(3), pages 1539-1558, May.
  • Handle: RePEc:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01356-2
    DOI: 10.1007/s00180-023-01356-2
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    References listed on IDEAS

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    1. Eric J. Bartelsman & Wayne Gray, 1996. "The NBER Manufacturing Productivity Database," NBER Technical Working Papers 0205, National Bureau of Economic Research, Inc.
    2. William Greene, 2003. "Simulated Likelihood Estimation of the Normal-Gamma Stochastic Frontier Function," Journal of Productivity Analysis, Springer, vol. 19(2), pages 179-190, April.
    3. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
    4. Schmidt, Peter & Sickles, Robin C, 1984. "Production Frontiers and Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 367-374, October.
    5. Efthymios G. Tsionas, 2007. "Efficiency Measurement with the Weibull Stochastic Frontier," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(5), pages 693-706, October.
    6. Ke Wang & Xin Ye, 2021. "Development of alternative stochastic frontier models for estimating time-space prism vertices," Transportation, Springer, vol. 48(2), pages 773-807, April.
    7. Waldman, Donald M., 1982. "A stationary point for the stochastic frontier likelihood," Journal of Econometrics, Elsevier, vol. 18(2), pages 275-279, February.
    8. Gholamreza Hajargasht, 2015. "Stochastic frontiers with a Rayleigh distribution," Journal of Productivity Analysis, Springer, vol. 44(2), pages 199-208, October.
    9. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    10. Cheol-Keun Cho & Peter Schmidt, 2020. "The wrong skew problem in stochastic frontier models when inefficiency depends on environmental variables," Empirical Economics, Springer, vol. 58(5), pages 2031-2047, May.
    11. Wang, Tonghui & Li, Baokun & Gupta, Arjun K., 2009. "Distribution of quadratic forms under skew normal settings," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 533-545, March.
    12. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    13. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    14. Mahdi Teimouri, 2021. "EM algorithm for mixture of skew-normal distributions fitted to grouped data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(7), pages 1154-1179, May.
    15. ZELLNER, Arnold & KMENTA, Jan & DREZE, Jacques H., 1966. "Specification and estimation of Cobb-Douglas production function models," LIDAM Reprints CORE 12, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
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