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Poisson exposure model

Estimators for a Poisson exposure model

The two variances are
$$
\operatorname{var}(\widehat\theta_{LS})
=\frac{\theta S_3}{S_2^2},
\qquad
\operatorname{var}(\widehat\theta_{MLE})
=\frac\theta{S_1}.
$$
Since $S_2^2\leq S_1S_3$ by Cauchy-Schwarz, maximum likelihood has no larger variance, with equality when all positive exposures are equal.


Variance comparison for Poisson exposure estimators

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 4 / 17H / c / Solution

Variance comparison for Poisson exposure estimators

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Variance comparison for Poisson exposure estimators

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