IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v83y2020i2d10.1007_s00184-019-00722-9.html
   My bibliography  Save this article

Optimal designs in sparse linear models

Author

Listed:
  • Yimin Huang

    (Peking University)

  • Xiangshun Kong

    (Beijing Institute of Technology)

  • Mingyao Ai

    (Peking University)

Abstract

The Lasso approach is widely adopted for screening and estimating active effects in sparse linear models with quantitative factors. Many design schemes have been proposed based on different criteria to make the Lasso estimator more accurate. This article applies $$\varPhi _l$$Φl-optimality to the asymptotic covariance matrix of the Lasso estimator. Smaller mean squared error and higher power of significant hypothesis tests can be achieved. A theoretically converging algorithm is given for searching for $$\varPhi _l$$Φl-optimal designs, and modified by intermittent diffusion to avoid local solutions. Some simulations are given to support the theoretical results.

Suggested Citation

  • Yimin Huang & Xiangshun Kong & Mingyao Ai, 2020. "Optimal designs in sparse linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(2), pages 255-273, February.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:2:d:10.1007_s00184-019-00722-9
    DOI: 10.1007/s00184-019-00722-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-019-00722-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-019-00722-9?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. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    2. Steven G. Gilmour & Luzia A. Trinca, 2012. "Optimum design of experiments for statistical inference," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(3), pages 345-401, May.
    3. Tingni Sun & Cun-Hui Zhang, 2012. "Scaled sparse linear regression," Biometrika, Biometrika Trust, vol. 99(4), pages 879-898.
    4. 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.
    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. Tianxi Cai & T. Tony Cai & Zijian Guo, 2021. "Optimal statistical inference for individualized treatment effects in high‐dimensional models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 669-719, September.
    2. Adel Javanmard & Jason D. Lee, 2020. "A flexible framework for hypothesis testing in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 685-718, July.
    3. Jana Janková & Rajen D. Shah & Peter Bühlmann & Richard J. Samworth, 2020. "Goodness‐of‐fit testing in high dimensional generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 773-795, July.
    4. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    5. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    6. Wang, Yihe & Zhao, Sihai Dave, 2021. "A nonparametric empirical Bayes approach to large-scale multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    7. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    8. Philipp Bach & Victor Chernozhukov & Malte S. Kurz & Martin Spindler & Sven Klaassen, 2021. "DoubleML -- An Object-Oriented Implementation of Double Machine Learning in R," Papers 2103.09603, arXiv.org, revised Jun 2024.
    9. Peter Bühlmann & Domagoj Ćevid, 2020. "Deconfounding and Causal Regularisation for Stability and External Validity," International Statistical Review, International Statistical Institute, vol. 88(S1), pages 114-134, December.
    10. Adamek, Robert & Smeekes, Stephan & Wilms, Ines, 2023. "Lasso inference for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 235(2), pages 1114-1143.
    11. Claude Renaux & Laura Buzdugan & Markus Kalisch & Peter Bühlmann, 2020. "Hierarchical inference for genome-wide association studies: a view on methodology with software," Computational Statistics, Springer, vol. 35(1), pages 1-40, March.
    12. Myung Hwan Seo & Yoichi Arai & Taisuke Otsu, 2021. "Regression Discontinuity Design with Potentially Many Covariates," Working Paper Series no142, Institute of Economic Research, Seoul National University.
    13. Zemin Zheng & Jinchi Lv & Wei Lin, 2021. "Nonsparse Learning with Latent Variables," Operations Research, INFORMS, vol. 69(1), pages 346-359, January.
    14. Guo, Zijian & Kang, Hyunseung & Cai, T. Tony & Small, Dylan S., 2018. "Testing endogeneity with high dimensional covariates," Journal of Econometrics, Elsevier, vol. 207(1), pages 175-187.
    15. Lucas Janson & Rina Foygel Barber & Emmanuel Candès, 2017. "EigenPrism: inference for high dimensional signal-to-noise ratios," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1037-1065, September.
    16. Bai, Ray & Ghosh, Malay, 2018. "High-dimensional multivariate posterior consistency under global–local shrinkage priors," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 157-170.
    17. Tanin Sirimongkolkasem & Reza Drikvandi, 2019. "On Regularisation Methods for Analysis of High Dimensional Data," Annals of Data Science, Springer, vol. 6(4), pages 737-763, December.
    18. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Granger Causality Testing in High-Dimensional VARs: A Post-Double-Selection Procedure," Journal of Financial Econometrics, Oxford University Press, vol. 21(3), pages 915-958.
    19. Qing Zhou & Seunghyun Min, 2017. "Uncertainty quantification under group sparsity," Biometrika, Biometrika Trust, vol. 104(3), pages 613-632.
    20. Kaspar Wuthrich & Ying Zhu, 2019. "Omitted variable bias of Lasso-based inference methods: A finite sample analysis," Papers 1903.08704, arXiv.org, revised Sep 2021.

    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:spr:metrik:v:83:y:2020:i:2:d:10.1007_s00184-019-00722-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.