# Unbiased Estimator

• April 30th 2011, 11:42 AM
reflex
Unbiased Estimator
$f(x|\theta) = \left(\begin{array}{c}x-1\\m-1\end{array}\right)\theta^m(1-\theta)^{x-m}$ x = m, m+1, etc... and m>=2

I find the mle of $\theta = \frac{m}{x}$, so good so far...

The next part is to find a constant $a$ s.t.

$\tilda{\theta(X)} \equiv \frac{a}{X-1}$ is an unbiased estimator of $\theta$

I could just plug in the mle estimator to a and use that, but that doesn't feel correct.

Thanks!