IAI Actuarial Core Principles · Actuarial Statistics · Estimators and their properties
Two unbiased estimators of the same parameter have variances 12 and 8 respectively. What is the relative efficiency of the first estimator with respect to the second (variance of the second divided by the variance of the first)?
The relative efficiency is about 0.67, because 8 divided by 12 equals 0.667. The first estimator has the larger variance, so it is less efficient than the second. The value 1.5 would be the inverted ratio.
- A1.50
- B0.50
- C0.67Correct
- D0.80
- 1.33
Explanation
Efficiency of first relative to second = Var(second)/Var(first) = 8/12 = 0.667. The value 1.50 is the inverse, which gives efficiency of the second relative to the first.
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