MINIMAX CONFIDENCE BOUND OF THE NORMAL MEAN UNDER AN ASYMMETRIC LOSS FUNCTION

摘要

Let X_1,..., X_n be i.i.d. normal random variables with mean μ and variance σ~2 (N(μ, σ~2)). A problem of estimating μ is considered for the case that σ is known or unknown. An estimator μ_L is called a lower confidence bound at confidence level 1 - α (0 < α < 1/2) if P_θ(μ_L(X) < μ) ≥ 1 - α for all θ, where X = (X_1, . . . , X_n), and θ = μ with σ known, θ = (μ, σ) with σ unknown.