Estimation under -invariant quasi-convex loss

The classical point estimation problem is investigated under alternative loss functions which are quasi-convex and symmetric with respect to some subgroup of the orthogonal group in n. A characterization of better estimators is proved and applied to scale and translation families of estimators. Finally, it is shown that every minimum variance unbiased normal estimator is best unbiased under arbitrary loss being quasi-convex and symmetric about the origin.