Abstract #300583


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JSM 2002 Abstract #300583
Activity Number: 406
Type: Contributed
Date/Time: Thursday, August 15, 2002 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #300583
Title: Rao-Cramer Type Inequalities for Mean Squared Error of Prediction
Author(s): Tapan Nayak*+
Affiliation(s): George Washington University
Address: 2201 G. Street, NW, Washington, District of Columbia, 20052, USA
Keywords: Admissibility ; Bhattacharyya bound ; Fisher information ; Unbiasedness
Abstract:

Let Y be an observable random vector and Z be an unobservable random variable with joint density f_\theta(y, z), where \theta is an unknown parameter vector. Considering the problem of predicting Z based on Y, we derive a Rao-Cramer type lower bound for the mean squared error (MSE) of any given predictor of Z satisfying some regularity conditions. Under unbiasedness, the lower bound does not depend on the specific predictor, and the condition for attaining that bound can be utilized to easily identify the best unbiased predictors in some applications. Using the lower bound we develop a method for proving admissibility of predictors under squared error loss. Bhattacharyya type bounds, and extensions of the results for vector Z, are also discussed, and some examples illustrating the utility of the results are presented.


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