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After estimating the Lasso coefficients in linear regression. Should we expect that prediction is unbiased ?

For example, for a new point $ (x^*,y^*)$, Should we expect $ E(y^*)=x^*\hat{\beta}$ to be unbiased ?

Under the assumption that $\hat{\beta}$ is the Maximum Likelihood Estimator (i.e. we are able to reach the global maximizer)

If it is biased, what are common corrections ?

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Lasso is a good example where bias can be actually preferable.

Take a look at this question and it's answers:

When is a biased estimator preferable to unbiased one?

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