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A stein two-sample procedure for the general linear model with unequal error variances
Authors:Thomas A Bishop
Institution:Department of Statistics , Virginia Polytechnic Institute and State University , Blacksburg, Virginia, 24061
Abstract:The pronerties of the tests and confidence regions for the parameters in the classical general linear model depend upon the equality of the variances of the error terms. The level and power of tests and the confidence coefficients associated with confidence regions are vitiated when the assumption of equality is not true. Even when the error variances are equal the power of tests and the size of confidence regions depend upon the unknown common variance and hence are uncontrollable. This paper presents a two-stage procedure which yields tests and confidence regions which are completely independent of the variances of the errors and hence tests with controllable power and confidence regions of fixed controllable size are obtained.
Keywords:two-stage sampling  controllable power  simple linear regression  fixed size confidence regions
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