IDEAS home Printed from https://ideas.repec.org/p/ete/kbiper/630770.html
   My bibliography  Save this paper

Estimation of the boundary of a variable observed with symmetric error

Author

Listed:
  • Jean-Pierre Florens
  • Léopold Simar
  • Ingrid Van Keilegom

Abstract

Consider the model with , where tau is an unknown constant (the boundary of X), Z is a random variable defined on , epsilon is a symmetric error, and epsilon and Z are independent. Based on an iid sample of Y, we aim at identifying and estimating the boundary tau when the law of epsilon is unknown (apart from symmetry) and in particular its variance is unknown. We propose an estimation procedure based on a minimal distance approach and by making use of Laguerre polynomials. Asymptotic results as well as finite sample simulations are shown. The paper also proposes an extension to stochastic frontier analysis, where the model is conditional to observed variables. The model becomes , where Y is a cost, w(1) are the observed outputs and w(2) represents the observed values of other conditioning variables, so Z is the cost inefficiency. Some simulations illustrate again how the approach works in finite samples, and the proposed procedure is illustrated with data coming from post offices in France.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2018. "Estimation of the boundary of a variable observed with symmetric error," Working Papers of Department of Decision Sciences and Information Management, Leuven 630770, KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven.
    • Handle: RePEc:ete:kbiper:630770
    Note: paper number KBI_1831
    as

    Download full text from publisher

    File URL: https://lirias.kuleuven.be/retrieve/524834
    File Function: Published version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bertrand, Aurelie & Van Keilegom, Ingrid & Legrand, Catherine, 2017. "Flexible parametric approach to classical measurement error variance estimation without auxiliary data," LIDAM Discussion Papers ISBA 2017025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2020. "Robust frontier estimation from noisy data: A Tikhonov regularization approach," Econometrics and Statistics, Elsevier, vol. 14(C), pages 1-23.
    3. Kneip, Alois & Simar, Léopold & Van Keilegom, Ingrid, 2015. "Frontier estimation in the presence of measurement error with unknown variance," Journal of Econometrics, Elsevier, vol. 184(2), pages 379-393.
    4. Cazals, Catherine & Fève, Frédérique & Florens, Jean-Pierre & Simar, Léopold, 2016. "Nonparametric instrumental variables estimation for efficiency frontier," Journal of Econometrics, Elsevier, vol. 190(2), pages 349-359.
    5. Aurore Delaigle & Peter Hall, 2016. "Methodology for non-parametric deconvolution when the error distribution is unknown," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 231-252, January.
    6. 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.
    7. Goldenshluger, A. & Tsybakov, A., 2004. "Estimating the endpoint of a distribution in the presence of additive observation errors," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 39-49, June.
    8. 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.
    9. 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).
    10. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    11. Delaigle, A. & Gijbels, I., 2006. "Data-driven boundary estimation in deconvolution problems," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1965-1994, April.
    12. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
    13. Cristina Butucea & Pierre Vandekerkhove, 2014. "Semiparametric Mixtures of Symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 227-239, March.
    14. 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.
    15. Lucie Aarts & Piet Groeneboom & Geurt Jongbloed, 2007. "Estimating the Upper Support Point in Deconvolution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(3), pages 552-568, September.
    16. 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)

    Citations

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


    Cited by:

    1. Oleg Badunenko & Daniel J. Henderson, 2024. "Production analysis with asymmetric noise," Journal of Productivity Analysis, Springer, vol. 61(1), pages 1-18, February.
    2. Caitlin O’Loughlin & Léopold Simar & Paul W. Wilson, 2023. "Methodologies for assessing government efficiency," Chapters, in: António Afonso & João Tovar Jalles & Ana Venâncio (ed.), Handbook on Public Sector Efficiency, chapter 4, pages 72-101, Edward Elgar Publishing.
    3. Kamil Makieła & Błażej Mazur, 2020. "Bayesian Model Averaging and Prior Sensitivity in Stochastic Frontier Analysis," Econometrics, MDPI, vol. 8(2), pages 1-22, April.
    4. Léopold Simar & Paul W. Wilson, 2023. "Nonparametric, Stochastic Frontier Models with Multiple Inputs and Outputs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1391-1403, October.
    5. William C. Horrace & Yulong Wang, 2022. "Nonparametric tests of tail behavior in stochastic frontier models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 537-562, April.
    6. Jun Cai & William C. Horrace & Christopher F. Parmeter, 2024. "Penalized sieve estimation of zero‐inefficiency stochastic frontiers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 41-65, January.
    7. Kamil Makie{l}a & B{l}a.zej Mazur, 2020. "Stochastic Frontier Analysis with Generalized Errors: inference, model comparison and averaging," Papers 2003.07150, arXiv.org, revised Oct 2020.
    8. Kamil Makieła & Błażej Mazur, 2022. "Model uncertainty and efficiency measurement in stochastic frontier analysis with generalized errors," Journal of Productivity Analysis, Springer, vol. 58(1), pages 35-54, August.

    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. Kneip, Alois & Simar, Léopold & Van Keilegom, Ingrid, 2015. "Frontier estimation in the presence of measurement error with unknown variance," Journal of Econometrics, Elsevier, vol. 184(2), pages 379-393.
    2. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2020. "Robust frontier estimation from noisy data: A Tikhonov regularization approach," Econometrics and Statistics, Elsevier, vol. 14(C), pages 1-23.
    3. Jun Cai & William C. Horrace & Christopher F. Parmeter, 2021. "Density deconvolution with Laplace errors and unknown variance," Journal of Productivity Analysis, Springer, vol. 56(2), pages 103-113, December.
    4. Kneip, A. & Simar, L. & Van Keilegom I., 2010. "Boundary estimation in the presence of measurement error with unknown variance," LIDAM Discussion Papers ISBA 2010046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Frédérique Fève & Jean-Pierre Florens & Léopold Simar, 2023. "Proportional incremental cost probability functions and their frontiers," Empirical Economics, Springer, vol. 64(6), pages 2721-2756, June.
    6. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    7. Léopold Simar & Paul W. Wilson, 2023. "Nonparametric, Stochastic Frontier Models with Multiple Inputs and Outputs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1391-1403, October.
    8. Simar, Léopold & Vanhems, Anne & Van Keilegom, Ingrid, 2016. "Unobserved heterogeneity and endogeneity in nonparametric frontier estimation," Journal of Econometrics, Elsevier, vol. 190(2), pages 360-373.
    9. George Halkos & Nickolaos Tzeremes, 2013. "National culture and eco-efficiency: an application of conditional partial nonparametric frontiers," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 15(4), pages 423-441, October.
    10. Keshvari, Abolfazl & Kuosmanen, Timo, 2013. "Stochastic non-convex envelopment of data: Applying isotonic regression to frontier estimation," European Journal of Operational Research, Elsevier, vol. 231(2), pages 481-491.
    11. Jun Cai & William C. Horrace & Christopher F. Parmeter, 2024. "Penalized sieve estimation of zero‐inefficiency stochastic frontiers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 41-65, January.
    12. Camilla Mastromarco & Léopold Simar, 2021. "Latent heterogeneity to evaluate the effect of human capital on world technology frontier," Journal of Productivity Analysis, Springer, vol. 55(2), pages 71-89, April.
    13. Kuosmanen, Timo & Johnson, Andrew, 2017. "Modeling joint production of multiple outputs in StoNED: Directional distance function approach," European Journal of Operational Research, Elsevier, vol. 262(2), pages 792-801.
    14. repec:wvu:wpaper:10-09 is not listed on IDEAS
    15. Andor, Mark A. & Parmeter, Christopher & Sommer, Stephan, 2019. "Combining uncertainty with uncertainty to get certainty? Efficiency analysis for regulation purposes," European Journal of Operational Research, Elsevier, vol. 274(1), pages 240-252.
    16. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2020. "Fast and efficient computation of directional distance estimators," Annals of Operations Research, Springer, vol. 288(2), pages 805-835, May.
    17. Florens, Jean-Pierre & Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Nonparametric Frontier Estimation from Noisy Data," IDEI Working Papers 625, Institut d'Économie Industrielle (IDEI), Toulouse.
    18. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.
    19. Stefan Seifert, 2016. "Semi-Parametric Measures of Scale Characteristics of German Natural Gas-Fired Electricity Generation," Discussion Papers of DIW Berlin 1571, DIW Berlin, German Institute for Economic Research.
    20. Mastromarco, Camilla & Simar, Leopold, 2017. "Cross-Section Dependence and Latent Heterogeneity to Evaluate the Impact of Human Capital on Country Performance," LIDAM Discussion Papers ISBA 2017030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    21. Minegishi, Kota, 2013. "Explaining Production Heterogeneity By Contextual Environments: Two-Stage DEA Application to Technical Change Measurement," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150289, Agricultural and Applied Economics Association.

    More about this item

    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:ete:kbiper:630770. 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: library EBIB (email available below). General contact details of provider: https://feb.kuleuven.be/KBI .

    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.