Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X $ be observed data. Let $\hat{\theta}(X)$ be an unbiased estimate of $\theta$ and let T be a sucient statistic for $\theta$. Define the new estimator $\hat\theta^{*}$ of $\theta$,

$$ \hat\theta^{*}(X) =E(\hat\theta(X)| T) $$

Then, show that:

$ \hat\theta^{*}(X)$ is unbiased

share|cite|improve this question
Use that in general: $E[E[X\mid Y]]=E[X]$ whatever $X$ and $Y$ may be (such that the conditional expectation exists). – Stefan Hansen Sep 30 '12 at 14:59
related to… – Henry Sep 30 '12 at 15:50

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.