Sankhya: The Indian Journal of Statistics
2003, Volume 65, Pt. 1, 122--138
On Second Order Admissibility Of Estimators In The Presence Of Nuisance Parameter
Y. Takagi, Osaka Prefecture University, Japan
SUMMARY. Our main concern is second order admissibility of estimators for a scalar parameter of interest in statistical models with nuisance parameters. A second order admissible estimator, which does not depend on any orthogonal parametrization, is given in the general form under any loss function. In addition, it is shown that the estimator is asymptotically equivalent to the generalized Bayes estimator under a familiar noninformative prior, up to the order $ O_p(1/n) $.
AMS (1991) subject classification. 62C10, 62C15, 62F12.
Key words and phrases. Second order admissibility, nuisance parameter, parameter orthogonality, parametrization-invariance, generalized Bayes estimator, matching prior.