Question

Which of the following statements about the Lasso are true with respect to the OLS​ estimates?

A. For a single​ regressor, when the OLS estimator is far from​ zero, the Lasso estimator shrinks it toward​ 0; and, when the OLS estimator is sufficiently​ small, the Lasso estimator becomes exactly 0.
B. For a single​ regressor, when the OLS estimator is far from the true population parameter​ value, the Lasso estimator shrinks it toward this true​ value; and, when the OLS estimator is sufficiently​ small, the Lasso estimator shrinks it toward 0.
C. When the OLS estimator is​ large, the Lasso shrinks it less than​ ridge, but when the OLS estimator is​ small, the Lasso shrinks it more than ridge.
D. When the OLS estimator is​ large, the Lasso shrinks it more than​ ridge, but when the OLS estimator is​ small, the Lasso shrinks it less than ridge.

Answer 1

B and C

Explanation:

B - The purpose of LASSO is to shrink parameter estimates towards zero, lasso shrinkage causes the estimates of the non-zero coefficients to be biased towards zero.

C- Lasso shrinks more accurately than the ridge. In the case of multiple coefficients Lasso selects only some some features and reduces the coefficients of the others to zero. This is called feature selection and it's not a possible in the ridge.