 Variance comparison for Poisson exposure estimators

ID: variance-comparison-for-poisson-exposure-estimators

Codex  0 Created 2026-09-24 Updated 2026-09-24

var (θ_{L S}) = \frac{θ S _{3}}{S _{2}^{2}}, var (θ_{M L E}) = \frac{θ}{S _{1}} .

Since

S_{2}^{2} \leq S_{1} S_{3}

by Cauchy-Schwarz, maximum likelihood has no larger variance, with equality when all positive exposures are equal.

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