IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v155y2017icp165-179.html
   My bibliography  Save this article

Smooth predictive model fitting in regression

Author

Listed:
  • Burman, Prabir
  • Paul, Debashis

Abstract

We propose a smooth hypothesis-testing type method for model fitting in regression and develop its theoretical properties in a moderately high-dimensional setting. We derive the asymptotic behavior of the L2 prediction risk and the optimal choice of the threshold-determining parameter under the Gaussian regression framework with orthogonal covariates. When the covariates are not orthogonal, this method can be used in conjunction with some reasonable procedures for orthogonalizing the covariates, such as a stepwise regression coupled with the Gram–Schmidt procedure. Simulation results show that our proposed method often outperforms its competitors. Asymptotic approximation of the mean square error of the proposed estimator is obtained and it is shown that the optimal rate of convergence depends on the behavior of the smoothing function at zero.

Suggested Citation

  • Burman, Prabir & Paul, Debashis, 2017. "Smooth predictive model fitting in regression," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 165-179.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:165-179
    DOI: 10.1016/j.jmva.2016.12.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16302664
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.12.010?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. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    2. 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.
    3. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    4. Wang, Tao & Zhu, Lixing, 2011. "Consistent tuning parameter selection in high dimensional sparse linear regression," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1141-1151, August.
    5. Yingying Fan & Cheng Yong Tang, 2013. "Tuning parameter selection in high dimensional penalized likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 531-552, June.
    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)

    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. Kaixu Yang & Tapabrata Maiti, 2022. "Ultrahigh‐dimensional generalized additive model: Unified theory and methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 917-942, September.
    2. Yunxiao Chen & Xiaoou Li & Jingchen Liu & Zhiliang Ying, 2017. "Regularized Latent Class Analysis with Application in Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 660-692, September.
    3. Zhang, Tonglin, 2024. "Variables selection using L0 penalty," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    4. Zhang, Shucong & Zhou, Yong, 2018. "Variable screening for ultrahigh dimensional heterogeneous data via conditional quantile correlations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 1-13.
    5. 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.
    6. Lian, Heng, 2014. "Semiparametric Bayesian information criterion for model selection in ultra-high dimensional additive models," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 304-310.
    7. Chen, Yunxiao & Li, Xiaoou & Liu, Jingchen & Ying, Zhiliang, 2017. "Regularized latent class analysis with application in cognitive diagnosis," LSE Research Online Documents on Economics 103182, London School of Economics and Political Science, LSE Library.
    8. Fan, Rui & Lee, Ji Hyung & Shin, Youngki, 2023. "Predictive quantile regression with mixed roots and increasing dimensions: The ALQR approach," Journal of Econometrics, Elsevier, vol. 237(2).
    9. Gaorong Li & Liugen Xue & Heng Lian, 2012. "SCAD-penalised generalised additive models with non-polynomial dimensionality," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 681-697.
    10. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    11. Fei Jin & Lung-fei Lee, 2018. "Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices," Econometrics, MDPI, vol. 6(1), pages 1-24, February.
    12. Chen, Bin & Maung, Kenwin, 2023. "Time-varying forecast combination for high-dimensional data," Journal of Econometrics, Elsevier, vol. 237(2).
    13. Sakyajit Bhattacharya & Paul McNicholas, 2014. "A LASSO-penalized BIC for mixture model selection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 45-61, March.
    14. Huicong Yu & Jiaqi Wu & Weiping Zhang, 2024. "Simultaneous subgroup identification and variable selection for high dimensional data," Computational Statistics, Springer, vol. 39(6), pages 3181-3205, September.
    15. Qingliang Fan & Yaqian Wu, 2020. "Endogenous Treatment Effect Estimation with some Invalid and Irrelevant Instruments," Papers 2006.14998, arXiv.org.
    16. Luke Mosley & Idris A. Eckley & Alex Gibberd, 2022. "Sparse temporal disaggregation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2203-2233, October.
    17. Jeon, Jong-June & Kwon, Sunghoon & Choi, Hosik, 2017. "Homogeneity detection for the high-dimensional generalized linear model," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 61-74.
    18. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    19. Luoying Yang & Tong Tong Wu, 2023. "Model‐based clustering of high‐dimensional longitudinal data via regularization," Biometrics, The International Biometric Society, vol. 79(2), pages 761-774, June.
    20. Yang Feng & Qingfeng Liu, 2020. "Nested Model Averaging on Solution Path for High-dimensional Linear Regression," Papers 2005.08057, arXiv.org.

    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:155:y:2017:i:c:p:165-179. 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.