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Wuhan University Journal of Natural Sciences

, Volume 24, Issue 4, pp 277–282 | Cite as

Nonparametric Regression Combining Linear Structure

  • Yanli ZhangEmail author
  • Yunquan Song
  • Lu Lin
  • Xiuli Wang
Mathematics
  • 14 Downloads

Abstract

Nonparametric models are popular owing to their flexibility in model building and optimality in estimation. However nonparametric models have the curse of dimensionality and do not use any of the prior information. How to sufficiently mine structure information hidden in the data is still a challenging issue in model building. In this paper, we propose a parametric family of estimators which allows for penalizing deviation from linear structure. The new estimator can automatically capture the linear information underlying regressions function to avoid the curse of dimensionality and offers a smooth choice between the full non-parametric models and parametric models. Besides, the new estimator is the linear estimator when the model has linear structure, and it is the local linear estimator when the model has no linear structure. Compared with the complete nonparametric models, our estimator has smaller bias due to using linear structure information of the data. The new estimator is useful in higher dimensions; the usual nonparametric methods have the curse of dimensionality. Based on the projection framework, the theoretical results give the structure of the new estimator and simulation studies demonstrate the advantages of the new approach.

Key words

nonparametric full model nonlinear 

CLC number

O 212.4 

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Copyright information

© Wuhan University and Springer-Verlag GmbH Germany 2019

Authors and Affiliations

  1. 1.School of StatisticsShandong University of Finance and EconomicsJinan, ShandongChina
  2. 2.College of ScienceChina University of PetroleumQingdao, ShandongChina
  3. 3.Zhongtai Securities Institute for Financial StudiesShandong UniversityJinan, ShandongChina
  4. 4.School of Mathematics and StatisticsShandong Normal UniversityJinan, ShandongChina

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