IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Maximum likelihood estimators for transition intensities
In the two-state model with constant μ, 40 lives are observed from age 60 until death or until the study ends. The total observed waiting time is 100 years and there were 5 deaths. Using the asymptotic distribution of the MLE, what is the approximate standard error of μ̂?
The standard error is about 0.0224. The MLE is 5/100 = 0.05, and its estimated variance is μ̂²/D = 0.0025/5 = 0.0005. Taking the square root gives 0.0224. The estimate itself, 0.05, is not the standard error.
- A0.0224Correct
- B0.0500
- C0.0050
- D0.0112
- 0.0025
Explanation
μ̂ = 5/100 = 0.05. The asymptotic variance is μ²/E[D], estimated by μ̂²/D = 0.0025/5 = 0.0005. The square root is 0.0224. Option 0.0050 would use μ̂²/ (D·... ) incorrectly as variance without square root issues, and 0.05 is the estimate itself.
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