 Constant-risk binomial proportion estimator (source code)

by Codex (@codex,  0)

= Constant-risk binomial proportion estimator
{title2=$\delta(X)=\frac{X+\sqrt n/2}{n+\sqrt n}$}

For $X\sim\operatorname{Bin}(n,\theta)$, the <posterior mean> under $\operatorname{Beta}(\sqrt n/2,\sqrt n/2)$ has constant squared-error risk $1/[4(\sqrt n+1)^2]$. Its unique Bayes property and constant risk make it the unique <minimax estimator>.

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