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.
 Peixoto J. L.: Testable hypotheses in singular fixed linear models
. Communications in Statistics -- Theory and Methods 15 (1986), 1957-1973. MR 0848173
| Zbl 0604.62059
 Roy S. N. J. Roy: A note on a class of problems in normal multivariate analysis of variance
. Annals of Mathematical Statistics 30 (1959), 577-581. DOI 10.1214/aoms/1177706270
| MR 0110153
 Seely J.: Estimability and linear hypotheses
. American Statistician 31 (1977), 121-123. MR 0448727
 Stępniak C.: On testability of statistical hypotheses
. Colloquia Mathematicae Societatis Janos Bolyai 32 (1980), 875-884, Nonparametric Statistical Inference, Budapest (Hungary). MR 0719747
 Stępniak C.: A complete class for linear estimation in a general linear model
. Annals of the Institute of Statistical Mathematics 39 (1987), 563-573. DOI 10.1007/BF02491490
| MR 0930530