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# A Nonparametric Model of Frontiers

## Author

Listed:
• Carlos Martins-FIlho
• Feng Yao

## Abstract

In this paper we propose a nonparametric regression frontier model that assumes no specific parametric family of densities for the unobserved stochastic component that represents efficiency in the model. Nonparametric estimation of the regression frontier is obtained using a local linear estimator that is shown to be consistent and $\sqrt{nh_n}$ asymptotically normal under standard assumptions. The estimator we propose envelops the data but is not inherently biased as Free Disposal Hull - FDH or Data Envelopment Analysis - DEA estimators. It is also more robust to extreme values than the aforementioned estimators. A Monte Carlo study is performed to provide preliminary evidence on the estimator's finite sample properties and to compare its performance to a bias corrected FDH estimato

## Suggested Citation

• Carlos Martins-FIlho & Feng Yao, 2004. "A Nonparametric Model of Frontiers," Econometric Society 2004 Latin American Meetings 102, Econometric Society.
• Handle: RePEc:ecm:latm04:102
as

## Download full text from publisher

File URL: http://repec.org/esLATM04/up.16430.1081468379.pdf
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## References listed on IDEAS

as
1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, May.
2. GIJBELS, Irène & MAMMEN, Enno & PARK, Byeong U. & SIMAR, Léopold, 1997. "On estimation of monotone and concave frontier functions," CORE Discussion Papers 1997031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
3. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
4. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
5. Hadri, Kaddour, 1999. "Estimation of a Doubly Heteroscedastic Stochastic Frontier Cost Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 359-363, July.
6. Caudill, Steven B & Ford, Jon M & Gropper, Daniel M, 1995. "Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 105-111, January.
7. repec:cor:louvrp:-571 is not listed on IDEAS
8. Rafik Baccouche & Mokhtar Kouki, 2003. "Stochastic Production Frontier and Technical Inefficiency: A Sensitivity Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 22(1), pages 79-91, February.
9. 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.
10. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(06), pages 855-877, December.
11. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
12. 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.
13. 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.
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## More about this item

### Keywords

nonparametric regression frontier; local linear estimation; U statistics.;

### JEL classification:

• C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

### NEP fields

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