Constant-Risk Shrinkage

Let X ~ Binomial(9, p) with p unknown. Consider the estimator p̂ = (X + 3/2)/12 = (X + √n/2)/(n + √n) with n = 9. Compute its mean squared error E[(p̂ − p)²] when the true value is p = 1/10. Give a reduced fraction.

• bias
• combinatorial games
• distributions
• estimation
• variance

Source: The minimax estimator of a binomial proportion is a standard result in decision theory (Hodges and Lehmann, 1950). Statement written for AxiomIQ.