Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 3 , pp. 465-475

ISOMORPHISM OF QUADRATIC NORM AND PC ORDERING OF ESTIMATORS ADMITTING FIRST ORDER REPRESENTATIONS

By

PRANAB KUMAR SEN, University of North Carolina at Chapel Hill

SUMMARY. BAN estimators generally admit first order representations which insure them to be also asymptotically Pitman closest. For AN estimators admitting a first order representation, an ordering under the Pitman closeness measure is established and is shown to be isomorphic to the one under the usual quadratic norm. Multiparameter problems are also treated in the same vein.

AMS (1980) subject classification. 62F10, 62C99.

Key words and phrases. AN representation; Pitman closeness; quadratic norm; shrinkage estimation; transitivity.

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