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Parametric component detection and variable selection in varying-coefficient partially linear models

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  • Wang, Dewei
  • Kulasekera, K.B.

Abstract

In this paper we are concerned with detecting the true structure of a varying-coefficient partially linear model. The first issue is to identify whether a coefficient is parametric. The second issue is to select significant covariates in both nonparametric and parametric portions. In order to simultaneously address both issues, we propose to combine local linear smoothing and the adaptive LASSO and penalize both the coefficient functions and their derivatives using an adaptive L1 penalty. We give conditions under which this new adaptive LASSO consistently identifies the significant variables and parametric components along with estimation sparsity. Simulated and real data analysis demonstrate the proposed methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:117-129
    DOI: 10.1016/j.jmva.2012.05.006
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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.
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    4. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    5. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
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    7. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

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    2. Feng, Sanying & Xue, Liugen, 2015. "Model detection and estimation for single-index varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 227-244.
    3. Yunquan Song & Yaqi Liu & Hang Su, 2022. "Robust Variable Selection for Single-Index Varying-Coefficient Model with Missing Data in Covariates," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    4. Mingqiu Wang & Peixin Zhao & Xiaoning Kang, 2020. "Structure identification for varying coefficient models with measurement errors based on kernel smoothing," Statistical Papers, Springer, vol. 61(5), pages 1841-1857, October.
    5. Ciuperca, Gabriela, 2021. "Variable selection in high-dimensional linear model with possibly asymmetric errors," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    6. Feng, Sanying & He, Wenqi & Li, Feng, 2020. "Model detection and estimation for varying coefficient panel data models with fixed effects," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).

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