Minimax Estimation of the Function of Parameters in Normal Distribution

The estimation of the function θ = exp {αβ ＋ bσ^2} of parameters （μ,σ^2） in normal distribution N（μ, σ^2） is discussed. And when the prior distributions of μ and σ^2 are independent, under the loss function L（θ,δ） = （θ^-1 ± δ - 1）^2, the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.