Complete Consistency: A Testing Analogue of Estimator Consistency

Donald Andrews ()

The Review of Economic Studies, 1986, vol. 53, issue 2, 263-269

Abstract: In this note we introduce a weak optimality condition for tests, called complete consistency. We argue that complete consistency is a more appropriate weak optimality condition for tests than is test consistency. Complete consistency is a testing analogue of estimator consistency. It is shown that a sequence of estimators is consistent, if and only if certain tests based on the estimators (such as Wald or likelihood ratio tests) are completely consistent, for all simple null hypotheses. The above notwithstanding, the relationship between consistent and completely consistent tests shows that test consistency is a relevant concept. Consistent tests can be used to show the existence of, and to construct, completely consistent tests. Further, completely consistent tests cannot be generated from nested families of inconsistent tests.

Date: 1986
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