Stochastic non-convex envelopment of data: Applying isotonic regression to frontier estimation
Isotonic nonparametric least squares (INLS) is a regression method for estimating a monotonic function by fitting a step function to data. In the literature of frontier estimation, the free disposal hull (FDH) method is similarly based on the minimal assumption of monotonicity. In this paper, we link these two separately developed nonparametric methods by showing that FDH is a sign-constrained variant of INLS. We also discuss the connections to related methods such as data envelopment analysis (DEA) and convex nonparametric least squares (CNLS). Further, we examine alternative ways of applying isotonic regression to frontier estimation, analogous to corrected and modified ordinary least squares (COLS/MOLS) methods known in the parametric stream of frontier literature. We find that INLS is a useful extension to the toolbox of frontier estimation both in the deterministic and stochastic settings. In the absence of noise, the corrected INLS (CINLS) has a higher discriminating power than FDH. In the case of noisy data, we propose to apply the method of non-convex stochastic envelopment of data (non-convex StoNED), which disentangles inefficiency from noise based on the skewness of the INLS residuals. The proposed methods are illustrated by means of simulated examples.
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Volume (Year): 231 (2013)
Issue (Month): 2 ()
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- Kerstens, Kristiaan & Vanden Eeckaut, Philippe, 1999.
"Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit,"
European Journal of Operational Research,
Elsevier, vol. 113(1), pages 206-214, February.
- KERSTENS, Kristiaan & VANDEN EECKAUT, Philippe, 1997. "Estimating returns to scale using nonparametric deterministic technologies : a new method based on goodness-of-fit," CORE Discussion Papers 1997013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- Simar, L. & Wilson, P.W., 1999. "Statistical Inference in Nonparametric Frontier Models: the State of the Art," Papers 9904, Catholique de Louvain - Institut de statistique.
- Jürgen Hansohm & Xiaomi Hu, 2012. "A convergent algorithm for a generalized multivariate isotonic regression problem," Statistical Papers, Springer, vol. 53(1), pages 107-115, February.
- Leleu, Herve, 2006. "A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models," European Journal of Operational Research, Elsevier, vol. 168(2), pages 340-344, January.
- H. Leleu, 2006. "A linear programming framework for free disposal hull technologies and cost functions: primal and dual models," Post-Print hal-00204497, HAL.
- Greene, William H., 1980. "Maximum likelihood estimation of econometric frontier functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 27-56, May.
- Afriat, Sidney N, 1972. "Efficiency Estimation of Production Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(3), pages 568-598, October.
- Per Agrell & Jørgen Tind, 2001. "A Dual Approach to Nonconvex Frontier Models," Journal of Productivity Analysis, Springer, vol. 16(2), pages 129-147, September.
- Podinovski, V. V., 2004. "On the linearisation of reference technologies for testing returns to scale in FDH models," European Journal of Operational Research, Elsevier, vol. 152(3), pages 800-802, February.
- Peyrache, Antonio & Coelli, Tim, 2009. "Testing procedures for detection of linear dependencies in efficiency models," European Journal of Operational Research, Elsevier, vol. 198(2), pages 647-654, October.
- Antonio Peyrache & Tim Coelli, 2008. "Testing procedures for detection of linear dependencies in efficiency models," CEPA Working Papers Series WP022008, School of Economics, University of Queensland, Australia.
- Murray D. Smith, 2008. "Stochastic frontier models with dependent error components," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 172-192, 03.
- Henry Tulkens, 1993. "On FDH efficiency analysis: Some methodological issues and applications to retail banking, courts, and urban transit," Journal of Productivity Analysis, Springer, vol. 4(1), pages 183-210, June.
- Timmer, C P, 1971. "Using a Probabilistic Frontier Production Function to Measure Technical Efficiency," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 776-794, July-Aug..
- Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
- Timo Kuosmanen, 2008. "Representation theorem for convex nonparametric least squares," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 308-325, 07.
- 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.
- 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.
- Abolfazl Keshvari & Nasim Dehghan Hardoroudi, 2008. "An Extended Numeration Method For Solving Free Disposal Hull Models In Dea," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(05), pages 689-696.
- Kuosmanen, Timo, 2012. "Stochastic semi-nonparametric frontier estimation of electricity distribution networks: Application of the StoNED method in the Finnish regulatory model," Energy Economics, Elsevier, vol. 34(6), pages 2189-2199.
- 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.
- Léopold Simar & Valentin Zelenyuk, 2011. "Stochastic FDH/DEA estimators for frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(1), pages 1-20, August.
- Leopold Simar & Valentin Zelenyuk, 2008. "Stochastic FDH/DEA estimators for Frontier Analysis," Discussion Papers 8, Kyiv School of Economics.
- Laurens Cherchye & Timo Kuosmanen & Thierry Post, 2001. "FDH Directional Distance Functions with an Application to European Commercial Banks," Journal of Productivity Analysis, Springer, vol. 15(3), pages 201-215, January.
- Fan, Yanqin & Li, Qi & Weersink, Alfons, 1996. "Semiparametric Estimation of Stochastic Production Frontier Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 460-468, October.
- 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.
- Kumbhakar, Subal C. & Park, Byeong U. & Simar, Leopold & Tsionas, Efthymios G., 2007. "Nonparametric stochastic frontiers: A local maximum likelihood approach," Journal of Econometrics, Elsevier, vol. 137(1), pages 1-27, March.
- Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
- 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.
- H. Leleu, 2009. "Mixing DEA and FDH models together," Post-Print halshs-00481985, HAL.
- 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.
- Mekaroonreung, Maethee & Johnson, Andrew L., 2012. "Estimating the shadow prices of SO2 and NOx for U.S. coal power plants: A convex nonparametric least squares approach," Energy Economics, Elsevier, vol. 34(3), pages 723-732.
- Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
- Timo Kuosmanen & Mika Kortelainen, 2012. "Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints," Journal of Productivity Analysis, Springer, vol. 38(1), pages 11-28, August. Full references (including those not matched with items on IDEAS)
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