Lasso vs Ridge Shrinkage of One Coefficient

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Easy

Statistics

A single coefficient has OLS estimate $\hat\beta=0.8$ . For a penalty strength $\lambda=1$ , consider the two penalised problems

$\text{Ridge: }\min_\beta\ \tfrac12(\beta-\hat\beta)^2+\tfrac{\lambda}{2}\beta^2,\qquad \text{Lasso: }\min_\beta\ \tfrac12(\beta-\hat\beta)^2+\lambda|\beta| .$

Give the minimisers as a comma-separated list in the order ridge, lasso.

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