IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v236y2023i2s030440762300194x.html
   My bibliography  Save this article

Generalized linear models with structured sparsity estimators

Author

Listed:
  • Caner, Mehmet

Abstract

In this paper, we introduce structured sparsity estimators for use in Generalized Linear Models. Structured sparsity estimators in the least squares loss are introduced by Stucky and van de Geer (2018). Their proofs exclusively depend on their use of fixed design and normal errors. We extend their results to debiased structured sparsity estimators with Generalized Linear Model based loss through incorporating random design and non-sub Gaussian data. Structured sparsity estimation means that penalized loss functions with a possible sparsity structure in a norm. These norms include norms generated from convex cones.

Suggested Citation

  • Caner, Mehmet, 2023. "Generalized linear models with structured sparsity estimators," Journal of Econometrics, Elsevier, vol. 236(2).
    • Handle: RePEc:eee:econom:v:236:y:2023:i:2:s030440762300194x
    DOI: 10.1016/j.jeconom.2023.105478
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440762300194X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2023.105478?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    2. Shi, Chengchun & Song, Rui & Chen, Zhao & Li, Runze, 2019. "Linear hypothesis testing for high dimensional generalized linear models," LSE Research Online Documents on Economics 102108, London School of Economics and Political Science, LSE Library.
    3. Alexandre Belloni & Victor Chernozhukov & Christian Hansen & Whitney K. Newey, 2017. "Simultaneous confidence intervals for high-dimensional linear models with many endogenous variables," CeMMAP working papers 63/17, Institute for Fiscal Studies.
    4. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    5. Caner, Mehmet & Kock, Anders Bredahl, 2018. "Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso," Journal of Econometrics, Elsevier, vol. 203(1), pages 143-168.
    6. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    7. Sara Geer, 2014. "Weakly decomposable regularization penalties and structured sparsity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 72-86, March.
    8. Kock, Anders Bredahl, 2016. "Oracle inequalities, variable selection and uniform inference in high-dimensional correlated random effects panel data models," Journal of Econometrics, Elsevier, vol. 195(1), pages 71-85.
    9. Chiang, Harold D. & Sasaki, Yuya, 2019. "Causal inference by quantile regression kink designs," Journal of Econometrics, Elsevier, vol. 210(2), pages 405-433.
    10. 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.
    11. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
    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. Mehmet Caner & Kfir Eliaz, 2021. "Shoiuld Humans Lie to Machines: The Incentive Compatibility of Lasso and General Weighted Lasso," Papers 2101.01144, arXiv.org, revised Sep 2021.
    2. Guo, Xu & Li, Runze & Liu, Jingyuan & Zeng, Mudong, 2023. "Statistical inference for linear mediation models with high-dimensional mediators and application to studying stock reaction to COVID-19 pandemic," Journal of Econometrics, Elsevier, vol. 235(1), pages 166-179.
    3. Guo, Xu & Li, Runze & Liu, Jingyuan & Zeng, Mudong, 2024. "Reprint: Statistical inference for linear mediation models with high-dimensional mediators and application to studying stock reaction to COVID-19 pandemic," Journal of Econometrics, Elsevier, vol. 239(2).
    4. Liu, Jianyu & Yu, Guan & Liu, Yufeng, 2019. "Graph-based sparse linear discriminant analysis for high-dimensional classification," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 250-269.
    5. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    6. 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.
    7. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-Dimensional Econometrics and Regularized GMM," Papers 1806.01888, arXiv.org, revised Jun 2018.
    8. Khai X. Chiong & Hyungsik Roger Moon, 2017. "Estimation of Graphical Models using the $L_{1,2}$ Norm," Papers 1709.10038, arXiv.org, revised Oct 2017.
    9. Victor Chernozhukov & Chen Huang & Weining Wang, 2021. "Uniform Inference on High-dimensional Spatial Panel Networks," Papers 2105.07424, arXiv.org, revised Sep 2023.
    10. Alexandre Belloni & Mingli Chen & Victor Chernozhukov, 2016. "Quantile Graphical Models: Prediction and Conditional Independence with Applications to Systemic Risk," Papers 1607.00286, arXiv.org, revised Oct 2019.
    11. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    12. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    13. Michael C. Knaus, 2021. "A double machine learning approach to estimate the effects of musical practice on student’s skills," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 282-300, January.
    14. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP54/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Toshio Honda, 2021. "The de-biased group Lasso estimation for varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 3-29, February.
    16. Dong Liu & Changwei Zhao & Yong He & Lei Liu & Ying Guo & Xinsheng Zhang, 2023. "Simultaneous cluster structure learning and estimation of heterogeneous graphs for matrix‐variate fMRI data," Biometrics, The International Biometric Society, vol. 79(3), pages 2246-2259, September.
    17. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    18. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
    19. Hansen, Christian & Liao, Yuan, 2019. "The Factor-Lasso And K-Step Bootstrap Approach For Inference In High-Dimensional Economic Applications," Econometric Theory, Cambridge University Press, vol. 35(3), pages 465-509, June.
    20. Osamu Komori & Shinto Eguchi & John B. Copas, 2015. "Generalized t-statistic for two-group classification," Biometrics, The International Biometric Society, vol. 71(2), pages 404-416, June.

    More about this item

    Keywords

    Uniformity; Size and power of the test; Restrictions;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

    Statistics

    Access and download statistics

    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:econom:v:236:y:2023:i:2:s030440762300194x. 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/locate/jeconom .

    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.