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Complete Consistency: A Testing Analogue of Estimator Consistency

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  • Donald W. K. Andrews

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.

Suggested Citation

  • Donald W. K. Andrews, 1986. "Complete Consistency: A Testing Analogue of Estimator Consistency," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 263-269.
    • Handle: RePEc:oup:restud:v:53:y:1986:i:2:p:263-269.
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    Cited by:

    1. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    2. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    3. Humberto Moreira & Marcelo Moreira, 2016. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," CeMMAP working papers 25/16, Institute for Fiscal Studies.
    4. Byung-hill Jun & Hosin Song, 2019. "Tests for Detecting Probability Mass Points," Korean Economic Review, Korean Economic Association, vol. 35, pages 205-248.

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