Skip to main content
SpringerLink
Log in

Partially function linear error-in-response models with validation data

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper considers partial function linear models of the form Y = ∫ X(t)β(t)dt + g(T) with Y measured with error. The authors propose an estimation procedure when the basis functions are data driven, such as with functional principal components. Estimators of β(t) and g(t) with the primary data and validation data are presented and some asymptotic results are given. Finite sample properties are investigated through some simulation study and a real data application.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Engle R, Granger C, Rice J, et al., Nonparametric estimates of the relation between weather and electricity sales, J. Amer. Statist. Assoc., 1986, 81: 310–320.

    Article  Google Scholar 

  2. Aneiros Pérez G, González-Manteiga W, and Vieu P, Estimation and testing in a partial linear regression model under long-memory dependence, Bernoulli, 2004, 10(1): 49–78.

    Article  MathSciNet  MATH  Google Scholar 

  3. Ferraty F and Romain Y, The Oxford Handbook of Functional Data Analysis, Oxford University Press, Oxford, 2011.

    MATH  Google Scholar 

  4. Kong D H, Xue K J, Yao F, et al., Partially functional linear regression in high dimensions, Biometrika, 2016, 103(1): 147–159.

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang G C, Feng X N, and Chen M, Functional partial linear single-index model, Scand. J. Stat., 2016, 43: 261–274.

    Article  MathSciNet  MATH  Google Scholar 

  6. Shin H, Partial functional linear regression, J. Statist. Plann. Inference, 2009, 139: 3405–3418.

    Article  MathSciNet  MATH  Google Scholar 

  7. Aneiros Pérez G and Vieu P, Semi-functional partial linear regression, Statist. Probab. Lett., 2006, 76: 1102–1110.

    Article  MathSciNet  MATH  Google Scholar 

  8. Lian H, Functional partial linear regression, J. Nonparametr. Stat., 2011, 23(1): 115–128.

    Article  MathSciNet  MATH  Google Scholar 

  9. Yao F, Müller H G, and Wang J L, Functional data analysis for sparse longitudinal data, J. Amer. Statist. Assoc., 2011, 100: 577–590.

    Article  MathSciNet  MATH  Google Scholar 

  10. Hall P and Hosseini-Nasab M, On properties of functional principal components analysis, J. R. Stat. Soc. Ser. B, 2006, 68: 109–126.

    Article  MathSciNet  MATH  Google Scholar 

  11. Hall P, Müller H G, and Wang J L, Properties of principal component methods for functional and longitudinal data analysis, Ann. Statist., 2006, 34: 1493–1517.

    Article  MathSciNet  MATH  Google Scholar 

  12. Ramsay J and Silverman B, Functional Data Analysis, 2nd Edition, Springer, Berlin, 2005.

    Book  MATH  Google Scholar 

  13. Ash R B and Gardner M F, Topics in Stochastic Process, Academic Press, New York, 1975.

    MATH  Google Scholar 

  14. Xia Y, Tong H, Li W K, et al., An Adaptive Estimation of Dimension Reduction Space (with discussion), J. R. Stat. Soc. Ser. B, 2002, 64: 363–410.

    Article  MathSciNet  MATH  Google Scholar 

  15. Ferré L and Yao A, Smoothed functional sliced inverse regression, Statist. Sinica, 2005, 15: 665–685.

    MathSciNet  MATH  Google Scholar 

  16. Amato U, Antoniadis A, and De Feis I, Dimension reduction in functional regression with applications, Comput. Statist. Data Anal, 2006, 50: 2422–2446.

    Article  MathSciNet  MATH  Google Scholar 

  17. Hsing T and Ren H, An RKHS formulation of the inverse regression dimension reduction problem, Ann.Statist, 2009, 37: 726–755.

    Article  MathSciNet  MATH  Google Scholar 

  18. Chen D, Hall P, and Müller H G, Single and multiple index functional regression models with nonparametric link, Ann. Statist., 2011, 39: 1720–1747.

    Article  MathSciNet  MATH  Google Scholar 

  19. Li Y H, Wang N Y, and Carroll R J, Generalized functional linear models with semiparametric single-index interactions, J. Amer. Statist. Assoc., 2010, 105: 621–633.

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang Q H, Estimation of partial linear error-in-variables model with validation data, J. Multivariate Anal., 1999, 69: 30–64.

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang Q H, Dimension reduction in partly linear error-in-response models with validation data, J. Multivariate Anal., 1999, 85: 234–252.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Guangxi University of Science and Technology, Liuzhou, 545006, China

    Tao Zhang & Jiafu Meng

  2. Guangxi Colleges and Universities Key Laboratory of Mathematics and Statistical Model, Guilin, 541004, China

    Tao Zhang

  3. School of Science, Guilin University of Technology, Guilin, 530001, China

    Bin Wang

Authors
  1. Tao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiafu Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tao Zhang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11561006 and 11471127, Master Foundation of Guangxi University of Technology under Grant No. 070235, Doctoral Foundation of Guangxi University of Science and Technology under Grant No. 14Z07, and Research Projects of Colleges and Universities in Guangxi under Grant No. KY2015YB171, the Open Fund Project of Guangxi Colleges and Universities Key Laboratory of Mathematics and Statistical Model under Grant No. 2016GXKLMS005.

This paper was recommended for publication by Editor SUN Liuquan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, T., Meng, J. & Wang, B. Partially function linear error-in-response models with validation data. J Syst Sci Complex 30, 734–750 (2017). https://doi.org/10.1007/s11424-017-5263-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-017-5263-0

Keywords

Search

Navigation