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.
Keywords
MathematicsNuisance parameterStatisticsSeries (stratigraphy)Chi-square testStatistical hypothesis testingTest (biology)EconometricsSimple (philosophy)Applied mathematics
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Publication Info
- Year
- 1987
- Type
- article
- Volume
- 74
- Issue
- 1
- Pages
- 33-43
- Citations
- 2062
- Access
- Closed
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Cite This
Robert B. Davies
(1987).
Hypothesis testing when a nuisance parameter is present only under the alternative.
Biometrika
, 74
(1)
, 33-43.
https://doi.org/10.1093/biomet/74.1.33
Identifiers
- DOI
- 10.1093/biomet/74.1.33