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Hypothesis testing when a nuisance parameter is present only under the alternative. (English) Zbl 0612.62023
A test statistic for a hypothesis, in the presence of a nuisance parameter \(\theta\) which enters the model only under the alternative, is developed which is chi-square distributed. As an example the author considers a time series subject to linear trend in which the alternative is that at least one changes its trend at some unknown time \(\theta\). Some other test statistics are also considered in this paper.
The simulation techniques have been used for the univariate continuous two phase problem and for the discrete frequency problem. Results for accurate test, approximate test and naive test are given and compared for large sample sizes and also for different series lengths.
Reviewer: B.L.Agarwal

62F03 Parametric hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)