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To show that an estimator can be consistent without being unbiased or even asymptotically unbiased, consider...

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 σ2, 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

(a) consistent; (b) neither unbiased nor asymptotically unbiased.

Math   Statistics-And-Probability   
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