IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v101y2014i2p269-284..html
   My bibliography  Save this article

Variance estimation in high-dimensional linear models

Author

Listed:
  • Lee H. Dicker

Abstract

The residual variance and the proportion of explained variation are important quantities in many statistical models and model fitting procedures. They play an important role in regression diagnostics and model selection procedures, as well as in determining the performance limits in many problems. In this paper we propose new method-of-moments-based estimators for the residual variance, the proportion of explained variation and other related quantities, such as the ℓ2 signal strength. The proposed estimators are consistent and asymptotically normal in high-dimensional linear models with Gaussian predictors and errors, where the number of predictors d is proportional to the number of observations n; in fact, consistency holds even in settings where d/n → ∞. Existing results on residual variance estimation in high-dimensional linear models depend on sparsity in the underlying signal. Our results require no sparsity assumptions and imply that the residual variance and the proportion of explained variation can be consistently estimated even when d>n and the underlying signal itself is nonestimable. Numerical work suggests that some of our distributional assumptions may be relaxed. A real-data analysis involving gene expression data and single nucleotide polymorphism data illustrates the performance of the proposed methods.

Suggested Citation

  • Lee H. Dicker, 2014. "Variance estimation in high-dimensional linear models," Biometrika, Biometrika Trust, vol. 101(2), pages 269-284.
  • Handle: RePEc:oup:biomet:v:101:y:2014:i:2:p:269-284.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/ast065
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    Citations

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


    Cited by:

    1. Wang, WenWu & Yu, Ping, 2017. "Asymptotically optimal differenced estimators of error variance in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 125-143.
    2. Saulius Jokubaitis & Remigijus Leipus, 2022. "Asymptotic Normality in Linear Regression with Approximately Sparse Structure," Mathematics, MDPI, vol. 10(10), pages 1-28, May.
    3. Xingyu Chen & Lin Liu & Rajarshi Mukherjee, 2024. "Method-of-Moments Inference for GLMs and Doubly Robust Functionals under Proportional Asymptotics," Papers 2408.06103, arXiv.org.
    4. Xin Wang & Lingchen Kong & Liqun Wang, 2022. "Estimation of Error Variance in Regularized Regression Models via Adaptive Lasso," Mathematics, MDPI, vol. 10(11), pages 1-19, June.
    5. 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.
    6. Hua Yun Chen & Hesen Li & Maria Argos & Victoria W. Persky & Mary E. Turyk, 2022. "Statistical Methods for Assessing the Explained Variation of a Health Outcome by a Mixture of Exposures," IJERPH, MDPI, vol. 19(5), pages 1-16, February.
    7. Sayanti Guha Majumdar & Anil Rai & Dwijesh Chandra Mishra, 2023. "Estimation of Error Variance in Genomic Selection for Ultrahigh Dimensional Data," Agriculture, MDPI, vol. 13(4), pages 1-16, April.
    8. He, Yi & Jaidee, Sombut & Gao, Jiti, 2023. "Most powerful test against a sequence of high dimensional local alternatives," Journal of Econometrics, Elsevier, vol. 234(1), pages 151-177.
    9. Yi He & Sombut Jaidee & Jiti Gao, 2020. "Most Powerful Test against High Dimensional Free Alternatives," Monash Econometrics and Business Statistics Working Papers 13/20, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    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:oup:biomet:v:101:y:2014:i:2:p:269-284.. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.