# variance unbiased estimator

• Feb 17th 2010, 07:32 AM
kesk717
variance unbiased estimator
Show that the mean of a random sample of size n is a minimum variance unbiased estimator of "lambda", of a Poisson distribution.

Can anybody provide some help for me?
• Feb 17th 2010, 11:56 AM
statmajor
You'll need to use the Lehmann–Scheffé theorem which states that if Y is a complete sufficient statistic for lambda, and there exists a function of Y such that this function is an unbiased estimator of lambda, then this function is an MVUE of lambda.

1. Find a complete sufficient statistic (Y) for lambda
2. Find a function of Y such that this function is an unbiased estimator of lambda.
• Feb 19th 2010, 01:52 PM
kesk717
Can somebody give me some more detailed advice? I am still having trouble with this
• Feb 19th 2010, 02:09 PM
statmajor
Fine. Here's a hint: The complete sufficient statistic for a poisson distribution is $\Sigma^n_1 X_i = n \overline{X}$. What's the expecation of $\Sigma^n_1 X_i$?