What's The Big Idea? Ridge Regression and Regularisation

Vinod, Hrishikesh D.

doi:10.1111/1740-9713.01472

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2021

2023

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Cited by 5 publications

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“…It is also a biased nonlinear shrinkage estimator. Vinod (2020) explains the "big idea" behind ridge regression, and concludes with a quote from Hastie (2020): "What started out as a simple fix for wayward linear regression models has evolved into a large collection of tools for data modeling. It would be hard to imagine the life of a data scientist without them.…”

Section: Introductionmentioning

confidence: 99%

Material Facts Obscured in Hansen's Modern Gauss-Markov Theorem

Vinod¹

2022

Preprint

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We show that the abstract and conclusion of Hansen's Econometrica paper, Hansen (2022), entitled a modern Gauss-Markov theorem (MGMT), obscures a material fact, which in turn can confuse students. The MGMT places ordinary least squares (OLS) back on a high pedestal by bringing in the Cramer-Rao efficiency bound. We explain why linearity and unbiasedness are linked, making most nonlinear estimators biased. Hence, MGMT extends the reach of the century-old GMT by a near-empty set. It misleads students because it misdirects attention back to the unbiased OLS from beneficial shrinkage and other tools, which reduce the mean squared error (MSE) by injecting bias.

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Section: Introductionmentioning

confidence: 99%