IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/22897.html
   My bibliography  Save this paper

Nonparametric Frontier Estimation from Noisy Data

Author

Listed:
  • Florens, Jean-Pierre
  • Schwarz, Maik
  • Van Bellegem, Sébastien

Abstract

A new nonparametric estimator of production a frontier is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied through simulated data.

Suggested Citation

  • Florens, Jean-Pierre & Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Nonparametric Frontier Estimation from Noisy Data," TSE Working Papers 10-179, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:22897
    as

    Download full text from publisher

    File URL: http://www.tse-fr.eu/sites/default/files/medias/doc/wp/etrie/10-179.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    2. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2012. "Regularization of nonparametric frontier estimators," Journal of Econometrics, Elsevier, vol. 168(2), pages 285-299.
    3. Alexandra Daskovska & Léopold Simar & Sébastien Bellegem, 2010. "Forecasting the Malmquist productivity index," Journal of Productivity Analysis, Springer, vol. 33(2), pages 97-107, April.
    4. 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.
    5. Pierre-Philippe Combes & Thierry Mayer & Jacques-François Thisse, 2008. "Economic Geography: The Integration of Regions and Nations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00311000, HAL.
    6. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
    7. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    8. Jérémie Bigot & Sébastien Van Bellegem, 2009. "Log‐density Deconvolution by Wavelet Thresholding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 749-763, December.
    9. Park, Byeong U. & Sickles, Robin C. & Simar, Leopold, 2003. "Semiparametric-efficient estimation of AR(1) panel data models," Journal of Econometrics, Elsevier, vol. 117(2), pages 279-309, December.
    10. Léopold Simar, 2007. "How to improve the performances of DEA/FDH estimators in the presence of noise?," Journal of Productivity Analysis, Springer, vol. 28(3), pages 183-201, December.
    11. Kneip, Alois & Park, Byeong U. & Simar, Léopold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(6), pages 783-793, December.
    12. Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), 2008. "High Frequency Financial Econometrics," Studies in Empirical Economics, Springer, number 978-3-7908-1992-2, September.
    13. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(6), pages 855-877, December.
    14. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011. "Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator," Econometric Theory, Cambridge University Press, vol. 27(3), pages 522-545, June.
    15. Neumann, Michael H., 2007. "Deconvolution from panel data with unknown error distribution," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1955-1968, November.
    16. Huriot,Jean-Marie & Thisse,Jacques-François (ed.), 2009. "Economics of Cities," Cambridge Books, Cambridge University Press, number 9780521118279, September.
    17. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    18. Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Consistent density deconvolution under partially known error distribution," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 236-241, February.
    19. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
    20. Schwarz, M. & Van Bellegem, S., 2010. "Consistent density deconvolution under partially known error distribution," LIDAM Reprints ISBA 2010013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    21. Bruno de Borger & Kristiaan Kerstens & Wim Moesen & Jacques Vanneste, 1994. "A non-parametric Free Disposal Hull (FDH) approach to technical efficiency: an illustration of radial and graph efficiency measures and some sensitivity results," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 130(IV), pages 647-667, December.
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. NESTEROV, Yurii, 2011. "Random gradient-free minimization of convex functions," LIDAM Discussion Papers CORE 2011001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Dai, Xiaofeng, 2016. "Non-parametric efficiency estimation using Richardson–Lucy blind deconvolution," European Journal of Operational Research, Elsevier, vol. 248(2), pages 731-739.
    3. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Discussion Papers CORE 2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Leonardo Andrade Rocha & Ahmad Saeed Khan & Patrícia Verônica Pinheiro Sales Lima & Maria Ester Dal Poz & Fernando Porfirio Soares De Oliveira, 2016. "Corrupção, Burocracia E Outras Falhas Institucionais: O “Câncer” Da Inovação E Do Desenvolvimento," Anais do XLIII Encontro Nacional de Economia [Proceedings of the 43rd Brazilian Economics Meeting] 090, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    5. AGRELL, Per & KASPERZEC, Roman, 2010. "Dynamic joint investments in supply chains under information asymmetry," LIDAM Discussion Papers CORE 2010085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2010. "Iterative Regularization in Nonparametric Instrumental Regression," TSE Working Papers 10-184, Toulouse School of Economics (TSE).
    2. Gautier, Axel & Wauthy, Xavier, 2012. "Competitively neutral universal service obligations," Information Economics and Policy, Elsevier, vol. 24(3), pages 254-261.
    3. Pierre Pestieau & Maria Racionero, 2015. "Tagging with leisure needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 687-706, December.
    4. Bréchet, Thierry & Jouvet, Pierre-André & Rotillon, Gilles, 2013. "Tradable pollution permits in dynamic general equilibrium: Can optimality and acceptability be reconciled?," Ecological Economics, Elsevier, vol. 91(C), pages 89-97.
    5. Cremer, Helmuth & Gahvari, Firouz & Pestieau, Pierre, 2011. "Fertility, human capital accumulation, and the pension system," Journal of Public Economics, Elsevier, vol. 95(11), pages 1272-1279.
    6. Leroux, Marie-Louise & Ponthiere, Gregory, 2013. "Utilitarianism and unequal longevities: A remedy?," Economic Modelling, Elsevier, vol. 30(C), pages 888-899.
    7. A. Mauleon & Vincent Vannetelbosch & Cecilia Vergari, 2014. "Unions' Relative Concerns And Strikes In Wage Bargaining," Bulletin of Economic Research, Wiley Blackwell, vol. 66(4), pages 374-383, October.
    8. M.-L. Leroux & P. Pestieau, 2012. "The political economy of derived pension rights," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 19(5), pages 753-776, October.
    9. Per J. Agrell & Axel Gautier, 2017. "A Theory of Soft Capture," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(3), pages 571-596, July.
    10. Manzi, Jorge & San Martin, Ernesto & Van Bellegem, Sébastien, 2010. "School System Evaluation By Value-Added Analysis under Endogeneity," IDEI Working Papers 631, Institut d'Économie Industrielle (IDEI), Toulouse.
    11. Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    12. STEPHAN, Rüdiger, 2010. "An extension of disjunctive programming and its impact for compact tree formulations," LIDAM Discussion Papers CORE 2010045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. GILLIS, Nicolas & GLINEUR, François, 2010. "On the geometric interpretation of the nonnegative rank," LIDAM Discussion Papers CORE 2010051, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Moreno-Ternero, Juan D., 2011. "Voting over piece-wise linear tax methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 29-36, January.
    15. Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
    16. AGRELL, Per & KASPERZEC, Roman, 2010. "Dynamic joint investments in supply chains under information asymmetry," LIDAM Discussion Papers CORE 2010085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. DI SUMMA, Marco & WOLSEY, Laurence, 2010. "Mixing sets linked by bidirected paths," LIDAM Discussion Papers CORE 2010063, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. LUTTENS, Roland Iwan, 2010. "Lower bounds rule!," LIDAM Discussion Papers CORE 2010069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. DENUIT, Michel & EECKHOUDT, Louis & TSETLIN, Ilia & WINKLER, Robert L., 2010. "Multivariate concave and convex stochastic dominance," LIDAM Discussion Papers CORE 2010044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. GABSZEWICZ, Jean & TAROLA, Ornella, 2010. "Product innovation and market acquisition of firms," LIDAM Discussion Papers CORE 2010078, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • P42 - Political Economy and Comparative Economic Systems - - Other Economic Systems - - - Productive Enterprises; Factor and Product Markets; Prices

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tse:wpaper:22897. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.