I'm trying to solve this problem:
Let $X$ be a single sample from Geo($p$) where $p ∈ (0, 1)$. Find a minimax estimator for $p$ under the loss $L(p, δ(x)) = (p−δ(x))^2/ p(1−p)$ .
I'm trying to put different priors for $p$ and find one with constant risk. Because we know Bayesian estimator with constant risk is minimax. But all I got gives me sth like $\delta(X) = 1/X$ and it doesn't have constant risk. Is there any hint?