IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2011-014.html
   My bibliography  Save this paper

Difference based ridge and Liu type estimators in semiparametric regression models

Author

Listed:
  • Duran, Esra Akdeniz
  • Härdle, Wolfgang Karl
  • Osipenko, Maria

Abstract

We consider a difference based ridge regression estimator and a Liu type estimator of the regression parameters in the partial linear semiparametric regression model, y = Xb + f + e. Both estimators are analysed and compared in the sense of mean-squared error. We consider the case of independent errors with equal variance and give conditions under which the proposed estimators are superior to the unbiased difference based estimation technique. We extend the results to account for heteroscedasticity and autocovariance in the error terms. Finally, we illustrate the performance of these estimators with an application to the determinants of electricity consumption in Germany.

Suggested Citation

  • Duran, Esra Akdeniz & Härdle, Wolfgang Karl & Osipenko, Maria, 2011. "Difference based ridge and Liu type estimators in semiparametric regression models," SFB 649 Discussion Papers 2011-014, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2011-014
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/56655/1/65479037X.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gülin Tabakan & Fikri Akdeniz, 2010. "Difference-based ridge estimator of parameters in partial linear model," Statistical Papers, Springer, vol. 51(2), pages 357-368, June.
    2. Hu Yang & Jianwen Xu, 2009. "An alternative stochastic restricted Liu estimator in linear regression," Statistical Papers, Springer, vol. 50(3), pages 639-647, June.
    3. 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.
    4. Fan, Jianqing & Wu, Yichao, 2008. "Semiparametric Estimation of Covariance Matrixes for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1520-1533.
    5. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    6. You, Jinhong & Chen, Gemai & Zhou, Yong, 2007. "Statistical inference of partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1539-1557, September.
    7. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
    8. Eubank, R. L. & Kambour, E. L. & Kim, J. T. & Klipple, K. & Reese, C. S. & Schimek, M., 1998. "Estimation in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 27-34, November.
    9. Yatchew,Adonis, 2003. "Semiparametric Regression for the Applied Econometrician," Cambridge Books, Cambridge University Press, number 9780521812832, January.
    10. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, November.
    11. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    12. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    13. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    14. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, November.
    15. M. Hubert & P. Wijekoon, 2006. "Improvement of the Liu estimator in linear regression model," Statistical Papers, Springer, vol. 47(3), pages 471-479, June.
    16. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    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. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Zanin, Luca, 2023. "A flexible estimation of sectoral portfolio exposure to climate transition risks in the European stock market," Journal of Behavioral and Experimental Finance, Elsevier, vol. 39(C).
    3. Liu, Jialuo & Chu, Tingjin & Zhu, Jun & Wang, Haonan, 2021. "Semiparametric method and theory for continuously indexed spatio-temporal processes," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    4. Sang, Peijun & Lockhart, Richard A. & Cao, Jiguo, 2018. "Sparse estimation for functional semiparametric additive models," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 105-118.
    5. Waleed B. Altukhaes & Mahdi Roozbeh & Nur A. Mohamed, 2024. "Robust Liu Estimator Used to Combat Some Challenges in Partially Linear Regression Model by Improving LTS Algorithm Using Semidefinite Programming," Mathematics, MDPI, vol. 12(17), pages 1-23, September.
    6. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    7. Dlugosz, Stephan & Mammen, Enno & Wilke, Ralf A., 2017. "Generalized partially linear regression with misclassified data and an application to labour market transitions," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 145-159.
    8. Morteza Amini & Mahdi Roozbeh & Nur Anisah Mohamed, 2024. "Separation of the Linear and Nonlinear Covariates in the Sparse Semi-Parametric Regression Model in the Presence of Outliers," Mathematics, MDPI, vol. 12(2), pages 1-17, January.
    9. Shirun Shen & Huiya Zhou & Kejun He & Lan Zhou, 2024. "Principal Component Analysis of Two-dimensional Functional Data with Serial Correlation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(3), pages 601-620, September.
    10. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    11. Timothy K.M. Beatty & Erling Røed Larsen, 2005. "Using Engel curves to estimate bias in the Canadian CPI as a cost of living index," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(2), pages 482-499, May.
    12. Gao, Lisa & Shi, Peng, 2022. "Leveraging high-resolution weather information to predict hail damage claims: A spatial point process for replicated point patterns," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 161-179.
    13. Qi Qian & Danh V. Nguyen & Esra Kürüm & Connie M. Rhee & Sudipto Banerjee & Yihao Li & Damla Şentürk, 2024. "Multivariate Varying Coefficient Spatiotemporal Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(3), pages 761-786, December.
    14. Yu Liu & Chin-Shang Li, 2023. "A linear spline Cox cure model with its applications," Computational Statistics, Springer, vol. 38(2), pages 935-954, June.
    15. Elizabeth Goult & Laura Andrea Barrero Guevara & Michael Briga & Matthieu Domenech de Cellès, 2024. "Estimating the optimal age for infant measles vaccination," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    16. Caldeira, João F. & Santos, André A.P. & Torrent, Hudson S., 2023. "Semiparametric portfolios: Improving portfolio performance by exploiting non-linearities in firm characteristics," Economic Modelling, Elsevier, vol. 122(C).
    17. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    18. Holland, Ashley D., 2017. "Penalized spline estimation in the partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 211-235.
    19. Benjamin Owusu & Bettina Bökemeier & Alfred Greiner, 2023. "Assessing nonlinearities and heterogeneity in debt sustainability analysis: a panel spline approach," Empirical Economics, Springer, vol. 64(3), pages 1315-1346, March.
    20. Degao Li & Guodong Li & Jinhong You, 2014. "Significant Variable Selection And Autoregressive Order Determination For Time-Series Partially Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 478-490, August.

    More about this item

    Keywords

    difference based estimator; differencing estimator; differencing matrix; Liu estimator; Liu type estimator; multicollinearity; ridge regression estimator; semiparametric model;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    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:zbw:sfb649:sfb649dp2011-014. 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/sohubde.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.