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

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

To show 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

σ

2

, 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 estimator

n

2

.

Show that this estimation procedure is

(a)

consistent; and

(b)

neither unbiased nor asymp-

totically unbiased.

math Statistics-And-Probability

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Answer 1

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