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Estimators for a Poisson exposure model

For

S_{r} = \sum_{i} x_{i}^{r}

, unweighted least squares through the origin and maximum likelihood give

θ_{L S} = \frac{\sum _{i} x _{i} Y _{i}}{S _{2}}, θ_{M L E} = \frac{\sum _{i} Y _{i}}{S _{1}} .

Both estimators are unbiased.

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- Variance comparison for Poisson exposure estimators Estimators for a Poisson exposure model 29

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