On a Normal Mean with Known Coefficient of Variation

Abstract

This paper deals with estimation of θ when iid (independent and identically distributed) observations are available from a N(θ,cθ²) distribution where c > 0 is assumed to be known. Using the equivariance principle under the group of scale and direction transformations we first characterize the class of equivariant estimators of θ. We then investigate a few equivariant estimators, including the maximum likelihood estimator, in terms of standardized bias and standardized mean squared error.