Estimation of an Exponential Quantile under a General Loss and an Alternative Estimator under Quadratic Loss

摘要

Estimation of the quantile μ + κσ of an exponential distribution with parameters (μ, σ) is considered under an arbitrary strictly convex loss function. For κ obeying a certain condition, the inadmissibility of the best affine equivariant procedure is established by exhibiting a better estimator. The LINEX loss is studied in detail. For quadratic loss, sufficient conditions are given for a scale equivariant estimator to dominate the best affine equivariant one and, when κ exceeds a lower bound specified below, a new minimax estimator is identified.