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Variable selection in high-dimensional linear model with possibly asymmetric errors

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  • Ciuperca, Gabriela

Abstract

In many application areas, the problem of the automatic variable selection in a linear model with asymmetric errors is encountered, when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least squares method is not appropriate and the quantile framework makes the inference more difficult because of the non differentiability of the loss function. An estimation method by penalizing the expectile process with an adaptive LASSO penalty is proposed and studied. Two cases are considered: first with the number of model parameters is assumed to be much smaller than the sample size and afterwards it could be of the same order; the two cases being distinct by the adaptive penalties considered. For each case, the rate convergence is obtained and the oracle properties of the adaptive LASSO expectile estimator are established. The proposed estimators are evaluated through Monte Carlo simulations and compared with the adaptive LASSO quantile estimator. The proposed estimation method is also applied to real data in genetics.

Suggested Citation

  • Ciuperca, Gabriela, 2021. "Variable selection in high-dimensional linear model with possibly asymmetric errors," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:csdana:v:155:y:2021:i:c:s0167947320302036
    DOI: 10.1016/j.csda.2020.107112
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Wang, Dewei & Kulasekera, K.B., 2012. "Parametric component detection and variable selection in varying-coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 117-129.
    3. Jun Zhao & Yi Zhang, 2018. "Variable selection in expectile regression," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(7), pages 1731-1746, April.
    4. Leng, Chenlei & Li, Bo, 2010. "Least squares approximation with a diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 254-261, February.
    5. Ruben Dezeure & Peter Bühlmann & Cun-Hui Zhang, 2017. "High-dimensional simultaneous inference with the bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 685-719, December.
    6. Zhao, Jun & Chen, Yingyu & Zhang, Yi, 2018. "Expectile regression for analyzing heteroscedasticity in high dimension," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 304-311.
    7. 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.
    8. Tang, Yanlin & Song, Xinyuan & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in high-dimensional quantile varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 115-132.
    9. Schnabel, Sabine K. & Eilers, Paul H.C., 2009. "Optimal expectile smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4168-4177, October.
    10. Gabriela Ciuperca, 2019. "Adaptive group LASSO selection in quantile models," Statistical Papers, Springer, vol. 60(1), pages 173-197, February.
    11. Zhang, Feipeng & Li, Qunhua, 2017. "A continuous threshold expectile model," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 49-66.
    12. Lina Liao & Cheolwoo Park & Hosik Choi, 2019. "Penalized expectile regression: an alternative to penalized quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 409-438, April.
    13. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    14. Jianqing Fan & Quefeng Li & Yuyan Wang, 2017. "Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 247-265, January.
    15. Rajen D. Shah & Peter Bühlmann, 2018. "Goodness‐of‐fit tests for high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 113-135, January.
    16. 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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    1. Gabriela Ciuperca, 2022. "Real-time detection of a change-point in a linear expectile model," Statistical Papers, Springer, vol. 63(4), pages 1323-1367, August.

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