Higher than second order approximations for sequential point estimation by a two-stage procedure

Abstract

We consider the sequential point estimation problem of the mean of a normal distribution N(μ, σ2) when the loss function is squared error plus linear cost. It is shown that a two-stage procedure has the asymptotic efficiency of which the order is higher than second order, provided the standard deviation has a known lower bound. We also give a higher than second-order approximation to the risk.