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Weighted ℓ1-penalized corrected quantile regression for high dimensional measurement error models

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  • Kaul, Abhishek
  • Koul, Hira L.

Abstract

Standard formulations of prediction problems in high dimension regression models assume the availability of fully observed covariates and sub-Gaussian and homogeneous model errors. This makes these methods inapplicable to measurement errors models where covariates are unobservable and observations are possibly non sub-Gaussian and heterogeneous. We propose a weighted penalized corrected quantile estimator for regression parameters in linear regression models with additive measurement errors, where unobservable covariate is nonrandom. The proposed estimators forgo the need for the above mentioned model assumptions. We study these estimators in a high dimensional sparse setup where the dimensionality can grow exponentially with the sample size. We provide bounds for the statistical error associated with the estimation, that hold with asymptotic probability 1, thereby providing the ℓ1-consistency of the proposed estimator. We also establish the model selection consistency in terms of the correctly estimated zero components of the parameter vector. A simulation study that investigates the finite sample accuracy of the proposed estimator is also included in the paper.

Suggested Citation

  • Kaul, Abhishek & Koul, Hira L., 2015. "Weighted ℓ1-penalized corrected quantile regression for high dimensional measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 72-91.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:72-91
    DOI: 10.1016/j.jmva.2015.04.009
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    References listed on IDEAS

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    2. Eun Ryung Lee & Hohsuk Noh & Byeong U. Park, 2014. "Model Selection via Bayesian Information Criterion for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 216-229, March.
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    Cited by:

    1. Alexandre Belloni & Victor Chernozhukov & Abhishek Kaul, 2017. "Confidence bands for coefficients in high dimensional linear models with error-in-variables," CeMMAP working papers CWP22/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Anish Agarwal & Keegan Harris & Justin Whitehouse & Zhiwei Steven Wu, 2023. "Adaptive Principal Component Regression with Applications to Panel Data," Papers 2307.01357, arXiv.org, revised Aug 2024.
    3. Ciuperca, Gabriela, 2021. "Variable selection in high-dimensional linear model with possibly asymmetric errors," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).

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