# Thread: T is to be an estimator for parameter theta

1. ## 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?

2. 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 $\displaystyle E(T_n)\to\theta$