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.

Question

Mathematics

Karla Ford

28 November, 08:56

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.

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Answers (1)

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Oliver Rubio · Answer 1

B and C

Step-by-step 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.