Admissible minimax model selection rule

This paper considers the problem of choosing one between the simple model N(0, I_d) and the full model N(0 I_d) based on the observation X from N(θ I_d) where X, θεR^d, 0 is the null vector in R^d and I_d is the d×d identity matrix. It is shown that the selection rule which chooses the full model if |x| > a_o , for some a₀ > 0 and the simple model otherwise is an admissible minimax model selection rule relative to a loss function which takes into account both inaccuracy and complexity.