Some properties of tests for parameters that can be arbitrarily close to being unidentified. (English) Zbl 1419.62505
Summary: Confidence intervals for parameters that can be arbitrarily close to being unidentified are unbounded with positive probability, and the asymptotic risks of their estimators are unbounded. We extend these “impossibility results” and show that all tests of size \(\alpha\) concerning parameters that can be arbitrarily close to being unidentified have power that can be as small as \(\alpha\) for any sample size even if the null and the alternative hypotheses are not adjacent. The results are proved for a very general framework that contains commonly used models.
MSC:
| 62P20 | Applications of statistics to economics |
| 62F03 | Parametric hypothesis testing |
| 62F25 | Parametric tolerance and confidence regions |
Keywords:
similar tests; consistent tests; uniformly consistent tests; identification; parameters arbitrarily close to being unidentifiedReferences:
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