IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Maximum likelihood estimators for transition intensities
In the two-state model with constant μ, the asymptotic variance of μ-hat is approximately μ²/E[D]. Another study has the same μ but observes four times as many expected deaths. Compared with the first study, the standard error of μ-hat in the second study is:
The standard error is halved. The asymptotic variance is inversely proportional to the expected number of deaths, so four times as many deaths gives a quarter of the variance, and the standard error, its square root, falls to one half.
- AOne quarter as large
- BFour times as large
- CUnchanged
- DHalf as largeCorrect
- One sixteenth as large
Explanation
Variance is μ²/E[D]. Quadrupling E[D] cuts the variance to a quarter. The standard error is the square root of the variance, so it is halved.
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