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Inference in high dimensional linear measurement error models

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  • Li, Mengyan
  • Li, Runze
  • Ma, Yanyuan

Abstract

For a high dimensional linear model with a finite number of covariates measured with errors, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and a corresponding score type estimator. This work was motivated by a real data example, where both low dimensional phenotypic variables and high dimensional genotypic variables, single nucleotide polymorphisms (SNPs), are available. One of the phenotypic variables is of clinical interest but measured with error. As is standard in the literature, the high dimensional SNPs are assumed to be measured accurately.

Suggested Citation

  • Li, Mengyan & Li, Runze & Ma, Yanyuan, 2021. "Inference in high dimensional linear measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jmvana:v:184:y:2021:i:c:s0047259x21000373
    DOI: 10.1016/j.jmva.2021.104759
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    References listed on IDEAS

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    1. Alexandre Belloni & Victor Chernozhukov & Abhishek Kaul, 2017. "Confidence bands for coefficients in high dimensional linear models with error-in-variables," CeMMAP working papers 22/17, Institute for Fiscal Studies.
    2. Alexandre Belloni & Mathieu Rosenbaum & Alexandre B. Tsybakov, 2017. "Linear and conic programming estimators in high dimensional errors-in-variables models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 939-956, June.
    3. Peter Hall & Yanyuan Ma, 2007. "Semiparametric estimators of functional measurement error models with unknown error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 429-446, June.
    4. Wang, Yining & Wang, Jialei & Balakrishnan, Sivaraman & Singh, Aarti, 2019. "Rate optimal estimation and confidence intervals for high-dimensional regression with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    5. Jianqing Fan & Lingzhou Xue & Hui Zou, 2016. "Multitask Quantile Regression Under the Transnormal Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1726-1735, October.
    6. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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    Cited by:

    1. Fan, Jinlin & Zhang, Yaowu & Zhu, Liping, 2022. "Independence tests in the presence of measurement errors: An invariance law," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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