IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v105y2012i1p164-175.html

Difference based ridge and Liu type estimators in semiparametric regression models

Author

Listed:
  • Akdeniz Duran, Esra
  • 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=Xβ+f+ε. Both estimators are analyzed 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

  • Akdeniz Duran, Esra & Härdle, Wolfgang Karl & Osipenko, Maria, 2012. "Difference based ridge and Liu type estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 164-175.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:164-175
    DOI: 10.1016/j.jmva.2011.08.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X11001862
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2011.08.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or

    for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, January.
    2. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    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. 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.
    5. Hu Yang & Jianwen Xu, 2009. "An alternative stochastic restricted Liu estimator in linear regression," Statistical Papers, Springer, vol. 50(3), pages 639-647, June.
    6. 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.
    7. Whitney Newey & Kenneth West, 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.
    8. 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.
    9. Yatchew,Adonis, 2003. "Semiparametric Regression for the Applied Econometrician," Cambridge Books, Cambridge University Press, number 9780521012263, January.
    10. 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.
    11. 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.
    12. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, January.
    13. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
    14. M. Hubert & P. Wijekoon, 2006. "Improvement of the Liu estimator in linear regression model," Statistical Papers, Springer, vol. 47(3), pages 471-479, June.
    15. 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.
    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)

    Citations

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


    Cited by:

    1. M. Arashi & Mahdi Roozbeh, 2019. "Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data," Statistical Papers, Springer, vol. 60(3), pages 667-686, June.
    2. Shao, Zhen & Gao, Fei & Zhang, Qiang & Yang, Shan-Lin, 2015. "Multivariate statistical and similarity measure based semiparametric modeling of the probability distribution: A novel approach to the case study of mid-long term electricity consumption forecasting i," Applied Energy, Elsevier, vol. 156(C), pages 502-518.
    3. Roozbeh, Mahdi, 2016. "Robust ridge estimator in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 127-144.
    4. Fikri Akdeniz & Mahdi Roozbeh, 2019. "Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models," Statistical Papers, Springer, vol. 60(5), pages 1717-1739, October.
    5. Roozbeh, Mahdi, 2018. "Optimal QR-based estimation in partially linear regression models with correlated errors using GCV criterion," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 45-61.
    6. Chien-Chia L. Huang & Yow-Jen Jou & Hsun-Jung Cho, 2017. "Difference-based matrix perturbation method for semi-parametric regression with multicollinearity," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2161-2171, September.
    7. Hadi Emami & Omid Khademnoe, 2025. "Shrinkage and pretest Liu estimators in semiparametric linear measurement error models," Statistical Papers, Springer, vol. 66(2), pages 1-35, February.
    8. Roozbeh, Mahdi, 2015. "Shrinkage ridge estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 56-74.
    9. Roozbeh, M. & Arashi, M., 2013. "Feasible ridge estimator in partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 35-44.
    10. Emami, Hadi, 2015. "Influence diagnostic in ridge semiparametric models," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 106-113.

    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. Dette, Holger & Marchlewski, Mareen, 2007. "A test for the parametric form of the variance function in apartial linear regression model," Technical Reports 2007,26, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    8. Vahid Goodarzi Vanani & Davood Shahsavani & Mohammad Kazemi, 2025. "A robust partial linear model combining modified Huber loss function and variable selection," Statistical Papers, Springer, vol. 66(6), pages 1-28, October.
    9. Kalogridis, Ioannis & Van Aelst, Stefan, 2023. "Robust penalized estimators for functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    10. Yuejin Zhou & Yebin Cheng & Wenlin Dai & Tiejun Tong, 2018. "Optimal difference-based estimation for partially linear models," Computational Statistics, Springer, vol. 33(2), pages 863-885, June.
    11. Goepp, Vivien & Bouaziz, Olivier & Nuel, Grégory, 2025. "Spline regression with automatic knot selection," Computational Statistics & Data Analysis, Elsevier, vol. 202(C).
    12. 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.
    13. 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.
    14. Hamid Mraoui & Ahmed El-Alaoui & Souad Bechrouri & Nezha Mohaoui & Abdelilah Monir, 2025. "Two-stage regression spline modeling based on local polynomial kernel regression," Computational Statistics, Springer, vol. 40(1), pages 383-403, January.
    15. Afonso, António & Alves, José & Beck, Krzysztof & Jackson, Karen, 2024. "Financial, institutional, and macroeconomic determinants of cross-country portfolio equity flows: The case of developed countries," Economic Modelling, Elsevier, vol. 141(C).
    16. Mark J. Meyer & Haobo Cheng & Katherine Hobbs Knutson, 2023. "Bayesian Analysis of Multivariate Matched Proportions with Sparse Response," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 490-509, July.
    17. Giancarlo Aquila & Lucas Barros Scianni Morais & Victor Augusto Durães de Faria & José Wanderley Marangon Lima & Luana Medeiros Marangon Lima & Anderson Rodrigo de Queiroz, 2023. "An Overview of Short-Term Load Forecasting for Electricity Systems Operational Planning: Machine Learning Methods and the Brazilian Experience," Energies, MDPI, vol. 16(21), pages 1-35, November.
    18. Nolan, Tui H. & Richardson, Sylvia & Ruffieux, Hélène, 2025. "Efficient Bayesian functional principal component analysis of irregularly-observed multivariate curves," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).
    19. Ioannis Kalogridis & Gerda Claeskens & Stefan Aelst, 2023. "Robust and efficient estimation of nonparametric generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 1055-1078, September.
    20. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.

    More about this item

    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

    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:eee:jmvana:v:105:y:2012:i:1:p:164-175. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.