I don't know how much help this will be, but from my stats textbook I found in the section on estimators that:
Which proves that is a biased estimator. However, note that it is asymptotically unbiased.
Suppose that constitute a random sample from a normal distribution with parameters and .
Q: Show that is a biased estimator of . Moreover, adjust to form an unbiased estimator for .
[Hint: Recall the distribution of and the result ].
A: Let . Since ~ we have that and . Furthermore, using the result in the hint and the fact that ~ we have that
.
So,
.
I am not sure what do do fro the second part of the question.
Am I doing this correctly?
Thanks, I found the algebra error in my derivation. Even so, I am still stuck on the second part. My thinking is I need to multiply by the reciprocal of the first part of the result, but I don't know what to do about getting rid of the gamma stuff.
Thanks for your help.