Challenging Estimation Question - Help needed
To show that an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the following estimation procedure: to estimate the mean of a population with the finite variance s2, we first take a random sample of size n. Then we randomly draw one of n slips of paper numbered from 1 through n, and if the number we draw is 2,3,…, or n, we use as our estimator the mean of the random sample; otherwise, we use the estimate n2. Show that this estimation procedure is
b) neither unbiased nor asymptotically unbiased.
Find the variance of this estimator.