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Local additive estimation

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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    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.

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