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general statistical hypothesis; strict unbiasedness; testability; linear hypotheses
The problem of testability has been undertaken many times in the context of linear hypotheses. Almost all these considerations restricted to some algebraical conditions without reaching the nature of the problem. Therefore, a general and commonly acceptable notion of testability is still wanted. Our notion is based on a simple and natural decision theoretic requirement and is characterized in terms of the families of distributions corresponding to the null and the alternative hypothesis. Its consequences in the case of linear hypotheses are discussed. Among other it is shown that some suggestions in statistical literature are unjustified.
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