IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v35y2016i8-10p1456-1470.html
   My bibliography  Save this article

The Risk of James--Stein and Lasso Shrinkage

Author

Listed:
  • Bruce E. Hansen

Abstract

This article compares the mean-squared error (or ℓ 2 risk) of ordinary least squares (OLS), James--Stein, and least absolute shrinkage and selection operator (Lasso) shrinkage estimators in simple linear regression where the number of regressors is smaller than the sample size. We compare and contrast the known risk bounds for these estimators, which shows that neither James--Stein nor Lasso uniformly dominates the other. We investigate the finite sample risk using a simple simulation experiment. We find that the risk of Lasso estimation is particularly sensitive to coefficient parameterization, and for a significant portion of the parameter space Lasso has higher mean-squared error than OLS. This investigation suggests that there are potential pitfalls arising with Lasso estimation, and simulation studies need to be more attentive to careful exploration of the parameter space.

Suggested Citation

  • Bruce E. Hansen, 2016. "The Risk of James--Stein and Lasso Shrinkage," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1456-1470, December.
    • Handle: RePEc:taf:emetrv:v:35:y:2016:i:8-10:p:1456-1470
    DOI: 10.1080/07474938.2015.1092799
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2015.1092799
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474938.2015.1092799?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. Cattaneo, Matias D. & Jansson, Michael & Newey, Whitney K., 2018. "Alternative Asymptotics And The Partially Linear Model With Many Regressors," Econometric Theory, Cambridge University Press, vol. 34(2), pages 277-301, April.
    2. Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, vol. 142(1), pages 201-211, January.
    3. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    4. 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.
    5. 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.
    6. Pötscher, Benedikt M. & Schneider, Ulrike, 2007. "On the distribution of the adaptive LASSO estimator," MPRA Paper 6913, University Library of Munich, Germany.
    7. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    8. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    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. Akio Namba, 2021. "Bootstrapping the Stein-Rule Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 219-237, December.
    2. Jorge Mejia & Shawn Mankad & Anandasivam Gopal, 2019. "A for Effort? Using the Crowd to Identify Moral Hazard in New York City Restaurant Hygiene Inspections," Information Systems Research, INFORMS, vol. 30(4), pages 1363-1386, December.
    3. Giuseppe Luca & Jan R. Magnus, 2021. "Weak Versus Strong Dominance of Shrinkage Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 239-266, December.

    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. Xianyi Wu & Xian Zhou, 2019. "On Hodges’ superefficiency and merits of oracle property in model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1093-1119, October.
    2. Marcelo C. Medeiros & Eduardo F. Mendes, 2015. "l1-Regularization of High-Dimensional Time-Series Models with Flexible Innovations," Textos para discussão 636, Department of Economics PUC-Rio (Brazil).
    3. Schneider Ulrike & Wagner Martin, 2012. "Catching Growth Determinants with the Adaptive Lasso," German Economic Review, De Gruyter, vol. 13(1), pages 71-85, February.
    4. Kun Chen & Kung-Sik Chan & Nils Chr. Stenseth, 2014. "Source-Sink Reconstruction Through Regularized Multicomponent Regression Analysis-With Application to Assessing Whether North Sea Cod Larvae Contributed to Local Fjord Cod in Skagerrak," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 560-573, June.
    5. Hui Xiao & Yiguo Sun, 2019. "On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study," JRFM, MDPI, vol. 12(3), pages 1-16, June.
    6. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    7. Tino Werner, 2022. "Asymptotic linear expansion of regularized M-estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 167-194, February.
    8. Pötscher, Benedikt M. & Schneider, Ulrike, 2008. "Confidence sets based on penalized maximum likelihood estimators," MPRA Paper 9062, University Library of Munich, Germany.
    9. Jie Ding & Vahid Tarokh & Yuhong Yang, 2018. "Model Selection Techniques -- An Overview," Papers 1810.09583, arXiv.org.
    10. Qin, Yichen & Wang, Linna & Li, Yang & Li, Rong, 2023. "Visualization and assessment of model selection uncertainty," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    11. Ruth M. Pfeiffer & Andrew Redd & Raymond J. Carroll, 2017. "On the impact of model selection on predictor identification and parameter inference," Computational Statistics, Springer, vol. 32(2), pages 667-690, June.
    12. 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.
    13. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    14. Yize Zhao & Matthias Chung & Brent A. Johnson & Carlos S. Moreno & Qi Long, 2016. "Hierarchical Feature Selection Incorporating Known and Novel Biological Information: Identifying Genomic Features Related to Prostate Cancer Recurrence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1427-1439, October.
    15. Gareth M. James & Peter Radchenko & Jinchi Lv, 2009. "DASSO: connections between the Dantzig selector and lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 127-142, January.
    16. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    17. Camila Epprecht & Dominique Guegan & Álvaro Veiga & Joel Correa da Rosa, 2017. "Variable selection and forecasting via automated methods for linear models: LASSO/adaLASSO and Autometrics," Post-Print halshs-00917797, HAL.
    18. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    19. 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.
    20. Peter Martey Addo & Dominique Guegan & Bertrand Hassani, 2018. "Credit Risk Analysis Using Machine and Deep Learning Models," Risks, MDPI, vol. 6(2), pages 1-20, April.

    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:taf:emetrv:v:35:y:2016:i:8-10:p:1456-1470. 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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    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.