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Additive partial linear models with measurement errors

Author

Listed:
  • Hua Liang
  • Sally W. Thurston
  • David Ruppert
  • Tatiyana Apanasovich
  • Russ Hauser

Abstract

We consider statistical inference for additive partial linear models when the linear covariate is measured with error. We propose attenuation-to-correction and simulation-extrapolation, simex, estimators of the parameter of interest. It is shown that the first resulting estimator is asymptotically normal and requires no undersmoothing. This is an advantage of our estimator over existing backfitting-based estimators for semiparametric additive models which require undersmoothing of the nonparametric component in order for the estimator of the parametric component to be root-n consistent. This feature stems from a decrease of the bias of the resulting estimator, which is appropriately derived using a profile procedure. A similar characteristic in semiparametric partially linear models was obtained by Wang et al. (2005). We also discuss the asymptotics of the proposed simex approach. Finite-sample performance of the proposed estimators is assessed by simulation experiments. The proposed methods are applied to a dataset from a semen study. Copyright 2008, Oxford University Press.

Suggested Citation

  • Hua Liang & Sally W. Thurston & David Ruppert & Tatiyana Apanasovich & Russ Hauser, 2008. "Additive partial linear models with measurement errors," Biometrika, Biometrika Trust, vol. 95(3), pages 667-678.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:667-678
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    File URL: http://hdl.handle.net/10.1093/biomet/asn024
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    Citations

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    Cited by:

    1. Song, Qiongxia & Yang, Lijian, 2010. "Oracally efficient spline smoothing of nonlinear additive autoregression models with simultaneous confidence band," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2008-2025, October.
    2. Zhangong Zhou & Rong Jiang & Weimin Qian, 2011. "Variable selection for additive partially linear models with measurement error," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 185-202, September.
    3. Dong, C. & Li, S., 2021. "Specification Lasso and an Application in Financial Markets," Cambridge Working Papers in Economics 2139, Faculty of Economics, University of Cambridge.
    4. Rong Chen & Hua Liang & Jing Wang, 2011. "Determination of linear components in additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 367-383.
    5. Guo, Jie & Tang, Manlai & Tian, Maozai & Zhu, Kai, 2013. "Variable selection in high-dimensional partially linear additive models for composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 56-67.
    6. Huang, Zhensheng & Pang, Zhen & Hu, Tao, 2013. "Testing structural change in partially linear single-index models with error-prone linear covariates," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 121-133.
    7. Dong, Hao & Otsu, Taisuke & Taylor, Luke, 2021. "Average Derivative Estimation Under Measurement Error," Econometric Theory, Cambridge University Press, vol. 37(5), pages 1004-1033, October.
    8. Chuan-hua Wei & Chunling Liu, 2012. "Statistical inference on semi-parametric partial linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 809-823, December.
    9. Rui Li & Yuanyuan Zhang, 2021. "Two-stage estimation and simultaneous confidence band in partially nonlinear additive model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1109-1140, November.
    10. Gressani, Oswaldo & Lambert, Philippe, 2020. "The Laplace-P-spline methodology for fast approximate Bayesian inference in additive partial linear models," LIDAM Discussion Papers ISBA 2020020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Li, Xinyi & Wang, Li & Nettleton, Dan, 2019. "Sparse model identification and learning for ultra-high-dimensional additive partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 204-228.
    12. Tang Qingguo & Chen Wenyu, 2022. "Estimation for partially linear additive regression with spatial data," Statistical Papers, Springer, vol. 63(6), pages 2041-2063, December.
    13. Boente, Graciela & Martínez, Alejandra Mercedes, 2023. "A robust spline approach in partially linear additive models," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    14. Lee, JooChul & Wang, HaiYing & Schifano, Elizabeth D., 2020. "Online updating method to correct for measurement error in big data streams," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    15. Heng Lian, 2012. "Variable selection in high-dimensional partly linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 825-839, December.
    16. Zhang, Jun & Zhou, Yan & Lin, Bingqing & Yu, Yao, 2017. "Estimation and hypothesis test on partial linear models with additive distortion measurement errors," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 114-128.
    17. Chuanhua Wei & Xiaonan Wang, 2016. "Liu-type estimator in semiparametric partially linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 459-468, September.

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