I'm not sure what your question is.
Also unbiased (1) is so is
and (3) is
Sorry about the naff title, couldn't think of anything else. So this question's on a past exam paper...
Suppose is to be used as an estimator for a parameter . Describe five criteria you would use to judge whether is a good estimator of .
So I have these five criteria written down:
Is that what the question's getting at?
- Unbiasedness; or, on average, the estimator is correct.
- Efficiency; or the estimator has a small variance.
- Consistency; where larger samples give more precise estimates i.e. and as
- Robustness/resistance; where the estimator will perform well even if the model isn't quite correct or there are outlying values in the data.
- Ease of calculation; since an estimator is more preferable if it is easy to calculate and understand.