Abstract #300147

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JSM 2003 Abstract #300147
Activity Number: 27
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
Sponsor: General Methodology
Abstract - #300147
Title: Sample Size Reduction for Two-Stage Estimation of a Linear Function of Mean Vectors
Author(s): Makoto Aoshima*+
Companies: University of Tsukuba
Address: Institute of Mathematics, Ibaraki 305-8571, , , Japan
Keywords: fixed-size confidence region ; second-order efficiency ; two-stage procedure
Abstract:

Aoshima, Takada, and Srivastava (JSPI 2002) solved the estimation problem for a linear function of mean vectors from multisample multivariate normal populations with covariance matrices completely unknown. Their solution gave a fixed-size confidence region, which has a fixed span with the preassigned confidence coefficient, by developing a Stein-type two-stage procedure [ATS]. However, it is known that a two-stage procedure tends to overestimate the optimal fixed-sample size while satisfying the probability requirement excessively and [ATS] is also not an exception to that. In this paper, it is shown that [ATS] cannot be asymptotically second-order efficient no matter how the initial sample size is chosen. To overcome this disadvantage, a method is given to reduce the sample-size required in a two-stage procedure and it is shown that the improved [ATS] by using that method successfully possesses the asymptotic second-order efficiency. The proposed method can be applied to other problems so that the experimenter would save the sample size as well as the cost caused by the sampling operations when using a two-stage procedure.

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