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Penalized empirical likelihood for high-dimensional partially linear varying coefficient model with measurement errors

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  • Fan, Guo-Liang
  • Liang, Han-Ying
  • Shen, Yu

Abstract

For the high-dimensional partially linear varying coefficient models where covariates in the nonparametric part are measured with additive errors, we, in this paper, study asymptotic distributions of a corrected empirical log-likelihood ratio function and maximum empirical likelihood estimator of the regression parameter. At the same time, based on penalized empirical likelihood (PEL) approach, the parameter estimation and variable selection of the model are investigated, the proposed PEL estimators are shown to possess the oracle property. Also, we introduce the PEL ratio statistic to test a linear hypothesis of the parameter and prove it follows an asymptotically chi-square distribution under the null hypothesis. Simulation study and real data analysis are undertaken to evaluate the finite sample performance of the proposed methods.

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  • Fan, Guo-Liang & Liang, Han-Ying & Shen, Yu, 2016. "Penalized empirical likelihood for high-dimensional partially linear varying coefficient model with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 183-201.
    • Handle: RePEc:eee:jmvana:v:147:y:2016:i:c:p:183-201
    DOI: 10.1016/j.jmva.2016.01.009
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    Cited by:

    1. Wang, Kangning & Li, Shaomin & Sun, Xiaofei & Lin, Lu, 2019. "Modal regression statistical inference for longitudinal data semivarying coefficient models: Generalized estimating equations, empirical likelihood and variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 257-276.
    2. Xu, Hong-Xia & Fan, Guo-Liang & Chen, Zhen-Long, 2017. "Hypothesis tests in partial linear errors-in-variables models with missing response," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 219-229.
    3. Xia Chen & Liyue Mao, 2020. "Penalized empirical likelihood for partially linear errors-in-variables models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 597-623, December.
    4. Bang-Qiang He & Xing-Jian Hong & Guo-Liang Fan, 2020. "Penalized empirical likelihood for partially linear errors-in-variables panel data models with fixed effects," Statistical Papers, Springer, vol. 61(6), pages 2351-2381, December.

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