IAI Actuarial Core Principles · Actuarial Statistics · Estimators and their properties
An estimator T of a parameter θ has bias 0.5 and variance 4. What is the mean squared error of T?
The mean squared error equals variance plus squared bias, so it is 4 + 0.25 = 4.25. Adding the bias without squaring it, or ignoring it, gives wrong values.
- A4.00
- B4.25Correct
- C4.50
- D3.75
- 2.25
Explanation
MSE = variance + bias² = 4 + 0.5² = 4.25. Option 4.00 ignores the bias, and 4.50 adds the bias instead of squaring it.
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