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Hypothesis testing when a nuisance parameter is present only under the alternative
Abstract
We wish to test a simple hypothesis against a family of alternatives indexed by a one-dimensional parameter, θ. We use a test derived from the corresponding family of test statistics appropriate for the case when θ is given. Davies (1977) introduced this problem when these test statistics had normal distributions. The present paper considers the case when their distribution is chi-squared. The results are applied to the detection of a discrete frequency component of unknown frequency in a time series. In addition quick methods for finding approximate significance probabilities are given for both the normal and chi-squared cases and applied to the two-phase regression problem in the normal case.
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Citations
Cited by
Threshold effects in non-dynamic panels: Estimation, testing, and inference
Hansen, B. E. (1999) · Journal of Econometrics · doi:10.1016/s0304-4076(99)00025-1 · Cited by 5,260
Tests for parameter instability and structural change with unknown change point.
Andrews, D. W. K. (1993) · Econometrica · doi:10.2307/2951764 · Cited by 4,334
Pauly, D., & Zeller, D. (2016) · Nature Communications · doi:10.1038/ncomms10244 · Cited by 1,313
Dynamic panels with threshold effect and endogeneity
Seo, M. H., & Shin, Y. (2016) · Journal of Econometrics · doi:10.1016/j.jeconom.2016.03.005 · Cited by 698
Jauk, E., Benedek, M., Dunst, B., & Neubauer, A. C. (2013) · Intelligence · doi:10.1016/j.intell.2013.03.003 · Cited by 476
Metadata
- Authors
- DAVIES, R. B.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1987
- Volume
- 74
- Issue
- 1
- Pages
- 33-43
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2131940376
- Cited by
- 2,056
- References
- 0
- FWCI
- 13.72
- Type
- journal article
- Language
- en
- Open access
- closed
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