You hold one dataset and two candidate estimators of the same quantity. Rule U is unbiased and has a large sampling variance. Rule B is biased and has a smaller sampling variance. You cannot see either rule's sampling distribution, because you have one dataset and do not know the truth. The field has no procedure that guarantees the lower mean squared error for every population and every sample size: section 13.2 shows that the winner depends on the size of the bias against the size of the variance, and section 13.6 shows that the best choice also moves with the sample size.
Take a position on this question: what procedure should choose between U and B, and what should the interval you report be allowed to promise?
In your answer: state what you compute from the data and what you assume to get it; say how you decide between the two rules; say what your reported interval covers and what it does not cover; and name one way your procedure could mislead you even when every step is followed.
Rubric. Tick each criterion your answer meets, then save the self-assessment. The platform does not grade it.
Worked solution
There is no single correct answer, so this is a model of the shape a complete answer takes, not a key. A level-3 answer begins by naming the quantity and the two rules. It splits the rows into a selection part and a report part, or it names an external dataset that supplies the bias model. On the selection part it estimates each rule's variance, either from a model of the data or by resampling, and it estimates the bias from the stated model or prior rather than from the same rows that will certify the winner. It then compares estimated mean squared errors and keeps one rule, with ties broken by a rule stated in advance.
The answer next says what the report promises. The interval is computed on the report part, after the rule is fixed. It covers the sampling variability of the chosen rule under the stated model in repeated samples; it does not cover the possibility that the model is wrong, that the bias estimate is wrong, or that the report rows differ from the population the reader cares about. The answer gives the cost: the selection part is removed from the report, so the interval is wider than it would be with all the rows, and a small selection part makes the choice between U and B noisy. It names a failure: if the bias model comes from a sample that is not representative, the chosen rule can be biased in a new way, and the interval will not show it because the interval never saw that error. A strong answer may repeat the split several times and report the spread, but it still says that the spread is an estimate, not a guarantee. The answer that scores 0 says only that bias and variance trade off and stops there.