An example is presented of an inadmissible best invariant point estimator of a location parameter. The extra moment condition of Brown and Fox (1974b) is violated. The example involves two independent, identically distributed observations, an improvement over Perng's (1970) example.
"An Inadmissible Best Invariant Estimator: The I.I.D. Case." Ann. Statist. 9 (5) 1127 - 1129, September, 1981. https://doi.org/10.1214/aos/1176345594