Hypothesis testing when a nuisance parameter is present only under the alternative

作者：Robert B. Davies · 发表于：Biometrika · 年份：1987 · DOI：10.1093/biomet/74.1.33 · 被引用次数：2089 · 研究领域：Advanced Statistical Methods and Models、Advanced Statistical Process Monitoring、Financial Risk and Volatility Modeling

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.