# Question

To show that an estimator can be consistent with-out 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.

(a) Consistent;

(b) Neither unbiased nor asymptotically unbiased.

## Answer to relevant Questions

If X1, X2, . . . , Xn constitute a random sample of size n from an exponential population, show that is a sufficient estimator of the parameter θ. If X1, X2, and X3 constitute a random sample of size n = 3 from a Bernoulli population, show that Y = X1 + 2X2 + X3 is not a sufficient estimator of θ. Consider special values of X1, X2, and X3.) Consider N independent random variables having identical binomial distributions with the parameters θ and n = 3. If no of them take on the value 0, n1 take on the value 1, n2 take on the value 2, and n3 take on the value 3, ...Given a random sample of size n from a Pareto population (see Exercise 6.21 on page 184), use the method of maximum likelihood to find a formula for estimating its parameter α. With reference to Exercise 10.72, check whether the following estimators are maximum likelihood estimators of θ: (a) 1/2 (Y1 + Yn); (b) 1/3 (Y1 + 2Y2). In exercise Let X1, X2, . . . , Xn be a random sample of size n from ...Post your question

0