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Partial linear single index models with distortion measurement errors

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Abstract

We study partial linear single index models when the response and the covariates in the parametric part are measured with errors and distorted by unknown functions of commonly observable confounding variables, and propose a semiparametric covariate-adjusted estimation procedure. We apply the minimum average variance estimation method to estimate the parameters of interest. This is different from all existing covariate-adjusted methods in the literature. Asymptotic properties of the proposed estimators are established. Moreover, we also study variable selection by adopting the coordinate-independent sparse estimation to select all relevant but distorted covariates in the parametric part. We show that the resulting sparse estimators can exclude all irrelevant covariates with probability approaching one. A simulation study is conducted to evaluate the performance of the proposed methods and a real data set is analyzed for illustration.

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Authors and Affiliations

  1. Shenzhen-Hong Kong Joint Centre for Applied Statistics Research, Shenzhen University, Shenzhen, 518060, China

    Jun Zhang

  2. Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, 14642, USA

    Yao Yu & Hua Liang

  3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

    Li-Xing Zhu

Authors
  1. Jun Zhang
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  2. Yao Yu
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  3. Li-Xing Zhu
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  4. Hua Liang
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Correspondence to Hua Liang.

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Zhang, J., Yu, Y., Zhu, LX. et al. Partial linear single index models with distortion measurement errors. Ann Inst Stat Math 65, 237–267 (2013). https://doi.org/10.1007/s10463-012-0371-z

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  • DOI: https://doi.org/10.1007/s10463-012-0371-z

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