Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 1 ,pp. 113--119

PARAMETRIZATION INVARIANCE WITH RESPECT TO SECOND ORDER ADMISSIBILITY UNDER GENERAL LOSS FUNCTION

By

YOSHIJI TAKAGI Osaka Prefecture University, Sakai

SUMMARY. Our main concern is on second order admissibility of estimators with respect to risk function under general loss functions. Whether a particular estimator such as the MLE or the bias-corrected MLE possesses this property depends on the choice of parameter and the functional form of loss function. A estimator with second order admissibility regardless of any parametrization is constructed in the form corresponding to a variety of loss functions.

AMS (1991) subject classification.62A05, 62C15, 62F12.

Key words and phrases. Second order admissibility, Parametrization invariance.

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