IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/1997100.html
   My bibliography  Save this paper

On adaptive estimation in partial linear models

Author

Listed:
  • Golubev, Georgi
  • Härdle, Wolfgang

Abstract

The problem of estimation of the finite dimensional parameter in a partial linear model is considered. We derive upper and lower bounds for the second minimax order risk and show that the second order minimax estimator is a penalized maximum likelihood estimator. It is well known that the performance of the estimator is depending on the choice of a smoothing parameter. We propose a practically feasible adaptive procedure for the penalization choice.

Suggested Citation

  • Golubev, Georgi & Härdle, Wolfgang, 1997. "On adaptive estimation in partial linear models," SFB 373 Discussion Papers 1997,100, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:1997100
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/66264/1/729738442.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hardle, W. & Nussbaum, M., 1990. "Kernel estimation: the equivalent spline smoothing method," LIDAM Discussion Papers CORE 1990013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    3. Härdle, W.K. & Mammen, E. & Müller, M.D., 1996. "Testing Parametric versus Semiparametric Modelling in Generalized Linear Models," Other publications TiSEM 3b9b6d39-869e-4ecd-9982-6, Tilburg University, School of Economics and Management.
    4. Härdle, W.K. & Mammen, E. & Müller, M.D., 1996. "Testing Parametric versus Semiparametric Modelling in Generalized Linear Models," Discussion Paper 1996-42, Tilburg University, Center for Economic Research.
    Full references (including those not matched with items on IDEAS)

    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. Michael C. Burda & Wolfgang Härdle & Marlene Müller & Axel Werwatz, 1998. "Semiparametric analysis of German East-West migration intentions: facts and theory," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 525-541.
    2. Härdle, Wolfgang & Müller, Marlene, 1997. "Multivariate and semiparametric kernel regression," SFB 373 Discussion Papers 1997,26, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Müller, Marlene, 1997. "Computer-assisted generalized partial linear models," SFB 373 Discussion Papers 1997,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Guang Cheng & Hao Zhang & Zuofeng Shang, 2015. "Sparse and efficient estimation for partial spline models with increasing dimension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 93-127, February.
    5. Atak, Alev & Linton, Oliver & Xiao, Zhijie, 2011. "A semiparametric panel model for unbalanced data with application to climate change in the United Kingdom," Journal of Econometrics, Elsevier, vol. 164(1), pages 92-115, September.
    6. Emiko Dupont & Simon N. Wood & Nicole H. Augustin, 2022. "Spatial+: A novel approach to spatial confounding," Biometrics, The International Biometric Society, vol. 78(4), pages 1279-1290, December.
    7. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    8. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    9. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    10. Wong, Heung & Liu, Feng & Chen, Min & Ip, Wai Cheung, 2009. "Empirical likelihood based diagnostics for heteroscedasticity in partial linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3466-3477, July.
    11. Qingming Zou & Zhongyi Zhu, 2014. "M-estimators for single-index model using B-spline," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 225-246, February.
    12. Roger D. Peng & Francesca Dominici & Thomas A. Louis, 2006. "Model choice in time series studies of air pollution and mortality," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 179-203, March.
    13. Boente, Graciela & Rodriguez, Daniela, 2008. "Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2808-2828, January.
    14. Schick, Anton, 1996. "Root-n consistent estimation in partly linear regression models," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 353-358, August.
    15. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 1998. "Semiparametric additive indices for binary response and generalized additive models," SFB 373 Discussion Papers 1998,95, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    16. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    17. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004. "Bootstrap Inference In Semiparametric Generalized Additive Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 265-300, April.
    18. Li, Chenxi, 2016. "Cause-specific hazard regression for competing risks data under interval censoring and left truncation," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 197-208.
    19. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    20. Gao, Jiti & Liang, Hua, 1995. "Asymptotic normality of pseudo-LS estimator for partly linear autoregression models," Statistics & Probability Letters, Elsevier, vol. 23(1), pages 27-34, April.

    More about this item

    Keywords

    ;
    ;
    ;

    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:zbw:sfb373:1997100. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.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.