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The Risk of James--Stein and Lasso Shrinkage

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  • 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.

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  • 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
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    References listed on IDEAS

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    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.

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