Re: 'Examine if estimator is unbiased'

Posted by Amit Goyal on May 29, 2014; 10:09am
URL: http://discussion-forum.276.s1.nabble.com/Examine-if-estimator-is-unbiased-tp7590905p7590975.html

Unbiasedness and consistency are two very different properties. Unbiasedness property says that the estimator on an average delivers the true value. Consistency says that as sample size increases the probability that the estimators delivers the value very different from the true one goes to zero. In other words, it delivers the value very close to true value with almost certainty when the sample size is high.
For example, in the problem that is considered above where we were trying to estimate theta:
Y = max{X(1), ... , X(n)} is a biased but consistent estimator  of theta.
And T = X(1) + X(n) is an unbiased but not a consistent estimator of theta.