IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v72y2010i2p171-191.html
   My bibliography  Save this article

Local additive estimation

Author

Listed:
  • Juhyun Park
  • Burkhardt Seifert

Abstract

Summary. Additive models are popular in high dimensional regression problems owing to their flexibility in model building and optimality in additive function estimation. Moreover, they do not suffer from the so‐called curse of dimensionality generally arising in non‐parametric regression settings. Less known is the model bias that is incurred from the restriction to the additive class of models. We introduce a new class of estimators that reduces additive model bias, yet preserves some stability of the additive estimator. The new estimator is constructed by localizing the additivity assumption and thus is named the local additive estimator. It follows the spirit of local linear estimation but is shown to be able to relieve partially the dimensionality problem. Implementation can be easily made with any standard software for additive regression. For detailed analysis we explicitly use the smooth backfitting estimator of Mammen, Linton and Nielsen.

Suggested Citation

  • Juhyun Park & Burkhardt Seifert, 2010. "Local additive estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 171-191, March.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:2:p:171-191
    DOI: 10.1111/j.1467-9868.2009.00731.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2009.00731.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9868.2009.00731.x?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
    ---><---

    References listed on IDEAS

    as
    1. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    2. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
    3. S. N. Wood, 2000. "Modelling and smoothing parameter estimation with multiple quadratic penalties," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 413-428.
    4. Breiman, Leo, 1993. "Fitting additive models to regression data : Diagnostics and alternative views," Computational Statistics & Data Analysis, Elsevier, vol. 15(1), pages 13-46, January.
    5. Jianqing Fan & Theo Gasser & Irène Gijbels & Michael Brockmann & Joachim Engel, 1997. "Local Polynomial Regression: Optimal Kernels and Asymptotic Minimax Efficiency," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 79-99, March.
    6. Axel Munk & Nicolai Bissantz & Thorsten Wagner & Gudrun Freitag, 2005. "On difference‐based variance estimation in nonparametric regression when the covariate is high dimensional," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 19-41, February.
    7. Spokoiny, Vladimir, 2002. "Variance Estimation for High-Dimensional Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 111-133, July.
    8. Opsomer, Jean D. & Ruppert, D., 1998. "A Fully Automated Bandwidth Selection Method for Fitting Additive Models," Staff General Research Papers Archive 1176, Iowa State University, Department of Economics.
    9. Jens Perch Nielsen & Stefan Sperlich, 2005. "Smooth backfitting in practice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 43-61, February.
    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. Lin, Lu & Song, Yunquan & Liu, Zhao, 2014. "Local linear–additive estimation for multiple nonparametric regressions," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 252-269.

    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. Suneel Babu Chatla, 2023. "Nonparametric inference for additive models estimated via simplified smooth backfitting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 71-97, February.
    2. Martins-Filho, Carlos & yang, ke, 2007. "Finite sample performance of kernel-based regression methods for non-parametric additive models under common bandwidth selection criterion," MPRA Paper 39295, University Library of Munich, Germany.
    3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    4. Joel L. Horowitz, 2012. "Nonparametric additive models," CeMMAP working papers CWP20/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Peter Malec, 2016. "A Semiparametric Intraday GARCH Model," Cambridge Working Papers in Economics 1633, Faculty of Economics, University of Cambridge.
    6. Joel L. Horowitz, 2012. "Nonparametric additive models," CeMMAP working papers 20/12, Institute for Fiscal Studies.
    7. Berthold R. Haag, 2008. "Non‐parametric Regression Tests Using Dimension Reduction Techniques," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 719-738, December.
    8. Xia Cui & Heng Peng & Songqiao Wen & Lixing Zhu, 2013. "Component Selection in the Additive Regression Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 491-510, September.
    9. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
    10. Lin, Huazhen & Pan, Lixian & Lv, Shaogao & Zhang, Wenyang, 2018. "Efficient estimation and computation for the generalised additive models with unknown link function," Journal of Econometrics, Elsevier, vol. 202(2), pages 230-244.
    11. Häggström, Jenny, 2013. "Bandwidth selection for backfitting estimation of semiparametric additive models: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 136-148.
    12. Mammen, Enno & Park, Byeong U. & Schienle, Melanie, 2012. "Additive models: Extensions and related models," SFB 649 Discussion Papers 2012-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Théophile T. Azomahou & Raouf Boucekkine & Bity Diene, 2009. "A closer look at the relationship between life expectancy and economic growth," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(2), pages 201-244, June.
    14. Su, Liangjun & Lu, Xun, 2013. "Nonparametric dynamic panel data models: Kernel estimation and specification testing," Journal of Econometrics, Elsevier, vol. 176(2), pages 112-133.
    15. Lin, Lu & Song, Yunquan & Liu, Zhao, 2014. "Local linear–additive estimation for multiple nonparametric regressions," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 252-269.
    16. Gayle, Wayne-Roy & Namoro, Soiliou Daw, 2013. "Estimation of a nonlinear panel data model with semiparametric individual effects," Journal of Econometrics, Elsevier, vol. 175(1), pages 46-59.
    17. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
    18. Li, Degui & Linton, Oliver & Lu, Zudi, 2015. "A flexible semiparametric forecasting model for time series," Journal of Econometrics, Elsevier, vol. 187(1), pages 345-357.
    19. Grith, Maria & Härdle, Wolfgang Karl & Kneip, Alois & Wagner, Heiko, 2016. "Functional principal component analysis for derivatives of multivariate curves," SFB 649 Discussion Papers 2016-033, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    20. Holger Dette & Matthias Guhlich & Natalie Neumeyer, 2015. "Testing for additivity in nonparametric quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 437-477, June.

    More about this item

    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:bla:jorssb:v:72:y:2010:i:2:p:171-191. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.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.