IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v112y2012icp117-129.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12001327
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.05.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    3. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    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.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Fang Lu & Jing Yang & Xuewen Lu, 2022. "One-step oracle procedure for semi-parametric spatial autoregressive model and its empirical application to Boston housing price data," Empirical Economics, Springer, vol. 62(6), pages 2645-2671, June.
    4. 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.
    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xuejun Ma & Yue Du & Jingli Wang, 2022. "Model detection and variable selection for mode varying coefficient model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 321-341, June.
    2. Ngai Hang Chan & Linhao Gao & Wilfredo Palma, 2022. "Simultaneous variable selection and structural identification for time‐varying coefficient models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 511-531, July.
    3. Jun Zhang & Zhenghui Feng & Peirong Xu & Hua Liang, 2017. "Generalized varying coefficient partially linear measurement errors models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 97-120, February.
    4. Weihua Zhao & Riquan Zhang & Jicai Liu, 2013. "Robust variable selection for the varying coefficient model based on composite L 1 -- L 2 regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 2024-2040, September.
    5. Xue-Jun Ma & Jing-Xiao Zhang, 2016. "A new variable selection approach for varying coefficient models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 59-72, January.
    6. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    7. Weihua Zhao & Weiping Zhang & Heng Lian, 2020. "Marginal quantile regression for varying coefficient models with longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 213-234, February.
    8. Heng Lian, 2012. "Variable selection in high-dimensional partly linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 825-839, December.
    9. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    10. Lai, Peng & Meng, Jie & Lian, Heng, 2015. "Polynomial spline approach for variable selection and estimation in varying coefficient models for time series data," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 21-27.
    11. Wongsa-art, Pipat & Kim, Namhyun & Xia, Yingcun & Moscone, Francesco, 2024. "Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    12. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    13. Chen, Bin & Maung, Kenwin, 2023. "Time-varying forecast combination for high-dimensional data," Journal of Econometrics, Elsevier, vol. 237(2).
    14. Abbas Khalili & Farhad Shokoohi & Masoud Asgharian & Shili Lin, 2023. "Sparse estimation in semiparametric finite mixture of varying coefficient regression models," Biometrics, The International Biometric Society, vol. 79(4), pages 3445-3457, December.
    15. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    16. Wei Lan & Ronghua Luo & Chih-Ling Tsai & Hansheng Wang & Yunhong Yang, 2015. "Testing the Diagonality of a Large Covariance Matrix in a Regression Setting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 76-86, January.
    17. Heng Lian & Xin Chen & Jian-Yi Yang, 2012. "Identification of Partially Linear Structure in Additive Models with an Application to Gene Expression Prediction from Sequences," Biometrics, The International Biometric Society, vol. 68(2), pages 437-445, June.
    18. Zhao, Weihua & Zhang, Riquan & Liu, Jicai & Hu, Hongchang, 2015. "Robust adaptive estimation for semivarying coefficient models," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 132-141.
    19. Xia, Xiaochao & Yang, Hu & Li, Jialiang, 2016. "Feature screening for generalized varying coefficient models with application to dichotomous responses," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 85-97.
    20. Lin, Lu & Zhu, Lixing & Gai, Yujie, 2016. "Inference for biased models: A quasi-instrumental variable approach," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 22-36.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:117-129. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.