IAI Actuarial Core Principles · Actuarial Statistics · Estimators and their properties
An estimator T of a parameter θ has bias 0.4 and variance 2.4. What is its mean squared error?
The mean squared error is 2.56. MSE equals the variance plus the square of the bias, so 2.4 plus 0.4 squared (0.16) gives 2.56. Adding the unsquared bias or ignoring it would give wrong values.
- A2.56Correct
- B2.80
- C2.00
- D2.40
- 2.64
Explanation
MSE = variance + bias^2 = 2.4 + 0.16 = 2.56. Adding the bias itself (2.4+0.4=2.8) is wrong because the bias must be squared. Ignoring the bias gives 2.4, which is only the variance.
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