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The practice of non-parametric estimation by solving inverse problems: the example of transformation models

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  • Frédérique Fève
  • Jean-Pierre Florens

Abstract

. This model is used as an example to illustrate the practice of the estimation by solving linear functional equations. This paper is specially focused on the data-driven selection of the regularization parameter and of the bandwidths. Simulations experiments illustrate the relevance of this approach. Copyright (C) 2010 The Author(s). The Econometrics Journal (C) 2010 Royal Economic Society

Suggested Citation

  • Frédérique Fève & Jean-Pierre Florens, 2010. "The practice of non-parametric estimation by solving inverse problems: the example of transformation models," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 1-27, October.
  • Handle: RePEc:ect:emjrnl:v:13:y:2010:i:3:p:s1-s27
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    References listed on IDEAS

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    1. Carrasco, Marine & Florens, Jean-Pierre, 2011. "A Spectral Method For Deconvolving A Density," Econometric Theory, Cambridge University Press, vol. 27(03), pages 546-581, June.
    2. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(03), pages 497-521, June.
    3. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
    4. Elena Argentesi & Lapo Filistrucchi, 2007. "Estimating market power in a two-sided market: The case of newspapers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(7), pages 1247-1266.
    5. Jean‐Pierre Florens & Jan Johannes & Sébastien Van Bellegem, 2012. "Instrumental regression in partially linear models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 304-324, June.
    6. Florens, Jean-Pierre & Sbaï, Erwann, 2010. "Local Identification In Empirical Games Of Incomplete Information," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1638-1662, December.
    7. Jean-Charles Rochet & Jean Tirole, 2014. "Platform Competition in Two-Sided Markets," CPI Journal, Competition Policy International, vol. 10.
    8. Peter Hall & Joel L. Horowitz, 2003. "Nonparametric methods for inference in the presence of instrumental variables," CeMMAP working papers CWP02/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. JOHANNES, Jan & VAN BELLEGHEM, Sébastien & VANHEMS, Anne, 2007. "A unified approach to solve ill-posed inverse problems in econometrics," CORE Discussion Papers 2007083, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    11. Joel L. Horowitz, 2007. "Asymptotic Normality Of A Nonparametric Instrumental Variables Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1329-1349, November.
    12. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    13. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2011. "Identification And Estimation By Penalization In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 27(03), pages 472-496, June.
    14. Richard Blundell & Joel L. Horowitz, 2007. "A Non-Parametric Test of Exogeneity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1035-1058.
    15. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    16. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    17. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
    18. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    19. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    20. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, July.
    21. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-137, January.
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    Citations

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    Cited by:

    1. Florens, Jean-Pierre & Sokullu, Senay, 2017. "Nonparametric Estimation Of Semiparametric Transformation Models," Econometric Theory, Cambridge University Press, vol. 33(04), pages 839-873, August.
    2. Fève, Frédérique & Florens, Jean-Pierre, 2014. "Non parametric analysis of panel data models with endogenous variables," Journal of Econometrics, Elsevier, vol. 181(2), pages 151-164.
    3. Van Keilegom, Ingrid & Vanhems, Anne, 2016. "Estimation of a semiparametric transformation model in the presence of endogeneity," TSE Working Papers 16-654, Toulouse School of Economics (TSE).
    4. Esmeralda A. Ramalho & Joaquim J. S. Ramalho, 2017. "Moment-based estimation of nonlinear regression models with boundary outcomes and endogeneity, with applications to nonnegative and fractional responses," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 397-420, April.
    5. Chiappori, Pierre-André & Komunjer, Ivana & Kristensen, Dennis, 2015. "Nonparametric identification and estimation of transformation models," Journal of Econometrics, Elsevier, vol. 188(1), pages 22-39.
    6. Florens, Jean-Pierre & Simoni, Anna, 2012. "Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior," Journal of Econometrics, Elsevier, vol. 170(2), pages 458-475.
    7. repec:adr:anecst:y:2017:i:128:p:67-108 is not listed on IDEAS
    8. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    9. Fève, Frédérique & Florens, Jean-Pierre, 2014. "Iterative algorithm for non parametric estimation of the instrumental variables quantiles," Economics Letters, Elsevier, vol. 123(3), pages 300-304.
    10. Florens, Jean-Pierre & Van Bellegem, Sébastien, 2015. "Instrumental variable estimation in functional linear models," Journal of Econometrics, Elsevier, vol. 186(2), pages 465-476.
    11. Van Keilegom, Ingrid & Vanhems, Anne, 2011. "Semiparametric transformation model with endogeneity: a control function approach," TSE Working Papers 11-243, Toulouse School of Economics (TSE).
    12. Senay SOKULLU & Sami STOULI, 2017. "Cross-Validation Selection of Regularisation Parameter(s) for Semiparametric Transformation Models," Annals of Economics and Statistics, GENES, issue 128, pages 67-108.
    13. Samuele Centorrino & Jean-Pierre Florens, 2014. "Nonparametric Instrumental Variable Estimation of Binary Response Models," Department of Economics Working Papers 14-07, Stony Brook University, Department of Economics.
    14. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, Department of Economics, University of Bristol, UK.
    15. 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.
    16. Van Bellegem, Sébastien & Florens, Jean-Pierre, 2014. "Instrumental variable estimation in functional linear models," CORE Discussion Papers 2014056, 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
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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