PARAMETRIZATION INVARIANCE WITH RESPECT TO SECOND ORDER ADMISSIBILITY UNDER MEAN SQUARED ERROR

YOSHIJI TAKAGI

College of Integrated Arts and Sciences, Osaka Prefecture University, Gakuencho 1-1, Sakai 599-8531, Japan

(Received October 14, 1996; revised November 17, 1997)

Abstract. Our main concern is about second order admissibility under mean squared error. A sufficient condition and a necessary condition for a modified maximum likelihood estimator to be second order admissible regardless of parametrization are obtained. In addition, some procedures for characterizing such estimators are provided.

Key words and phrases: Second order admissibility, parametrization invariance, mean squared error.