Minimum mean squared estimation of location and scale parameters under misspecification of the model

SUMMARY The paper is concerned with estimating location and scale parameters by estimators minimizing a mean squared distance between the empirical distribution function and a conveniently chosen parameterized-distribution function. Within the true parametric family the location estimator has the same asymptotic distribution as that of Hodges & Lehmann. If the underlying distribution is not a member of the assumed parametric family, the questions concerning bias, rather than variance, are dominant and most of the paper is concerned with this situation. Numerical results are given for the case of contaminated normal distributions.