Abstract
In this paper statistical tests with fuzzily formulated hypotheses are discussed, i.e., hypotheses H 0 and H 1 are fuzzy sets. The classical criteria of the errors of type I and type II are generalized, and this approach is applied to the linear hypothesis in the linear regression model. A sufficient condition to control both generalized criteria simultaneously is presented even in case of testing H 0 against the omnibus alternative H 1: -H 0. This is completely different from the classical case of testing crisp complementary hypotheses.
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Arnold, B.F., Gerke, O. Testing fuzzy linear hypotheses in linear regression models. Metrika 57, 81–95 (2003). https://doi.org/10.1007/s001840200201
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DOI: https://doi.org/10.1007/s001840200201