# T is to be an estimator for parameter theta

• Aug 12th 2009, 01:14 PM
chella182
T is to be an estimator for parameter theta
Sorry about the naff title, couldn't think of anything else. So this question's on a past exam paper...

Suppose $\displaystyle T$ is to be used as an estimator for a parameter $\displaystyle \theta$. Describe five criteria you would use to judge whether $\displaystyle T$ is a good estimator of $\displaystyle \theta$.

So I have these five criteria written down:
1. Unbiasedness; or, on average, the estimator is correct.
2. Efficiency; or the estimator has a small variance.
3. Consistency; where larger samples give more precise estimates i.e. $\displaystyle E[T]\rightarrow\mu$ and $\displaystyle Var(T)\rightarrow0$ as $\displaystyle n\rightarrow\infty$
4. Robustness/resistance; where the estimator will perform well even if the model isn't quite correct or there are outlying values in the data.
5. Ease of calculation; since an estimator is more preferable if it is easy to calculate and understand.
Is that what the question's getting at?
• Aug 12th 2009, 09:37 PM
matheagle
I'm not sure what your question is.
Also unbiased (1) is $\displaystyle E(T)=\theta$ so $\displaystyle \mu$ is $\displaystyle \theta$
and (3) is $\displaystyle E(T_n)\to\theta$