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An improved Afriat–Diewert–Parkan nonparametric production function estimator

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  • Olesen, O.B.
  • Ruggiero, J.

Abstract

Recent developments in the production frontier literature include nonparametric estimators with shape constraints. A few of these estimators rely on the Afriat inequalities to provide piecewise linear approximations to the production function/frontier. We show in this paper that these Afriat–Diewert–Parkan (ADP) estimators have deficiencies in the presence of moderate statistical noise including overfitting and a relatively high estimator variance. We propose new estimators with lower variance and a relatively low bias. We consider such alternative estimators based on (weighted) averages of random hinge functions with parameter restrictions. Small sample properties of the estimators are presented that show our new estimators outperform the existing ADP estimators when moderate to large amounts of noise are present.

Suggested Citation

  • Olesen, O.B. & Ruggiero, J., 2018. "An improved Afriat–Diewert–Parkan nonparametric production function estimator," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1172-1188.
    • Handle: RePEc:eee:ejores:v:264:y:2018:i:3:p:1172-1188
    DOI: 10.1016/j.ejor.2017.07.057
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    Cited by:

    1. Christopher F. Parmeter & Alan T. K. Wan & Xinyu Zhang, 2019. "Model averaging estimators for the stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 51(2), pages 91-103, June.
    2. José Luis Preciado Arreola & Daisuke Yagi & Andrew L. Johnson, 2020. "Insights from machine learning for evaluating production function estimators on manufacturing survey data," Journal of Productivity Analysis, Springer, vol. 53(2), pages 181-225, April.
    3. Olesen, O.B. & Ruggiero, J., 2022. "The hinging hyperplanes: An alternative nonparametric representation of a production function," European Journal of Operational Research, Elsevier, vol. 296(1), pages 254-266.
    4. Raul Moragues & Juan Aparicio & Miriam Esteve, 2023. "Measuring technical efficiency for multi-input multi-output production processes through OneClass Support Vector Machines: a finite-sample study," Operational Research, Springer, vol. 23(3), pages 1-33, September.
    5. Moragues, Raul & Aparicio, Juan & Esteve, Miriam, 2023. "An unsupervised learning-based generalization of Data Envelopment Analysis," Operations Research Perspectives, Elsevier, vol. 11(C).

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