$1($d$)$ Suppose that $y_{i}N(,1)$ for $i=1,2,$dotsn and are independent. An analyst plans to follow

the Lasso approach and use the estimator that minimizes

${\displaystyle \underset{i=1}{\overset{n}{}}}(y_i-{)}^2+||$

What is the bias and variance of such an estimator?

$50m$

$1($e$)$ Is the estimator above unbiased? Prove.

$[10$m$]$

$1($f$)$ Show if the estimator above has lower variance than the variance of the standard estimator

$\frac{{\displaystyle \underset{i=1}{\overset{n}{}}}{y}_i}{n}$

$10m$