Repeated significance tests for exponential families. (English) Zbl 0665.62081

Hu, Inchi

Ann. Stat. 16, No. 4, 1643-1666 (1988).

To test \(H_ 0:\theta \in \Theta_ 0\subset \Theta\), the sequence of log-likelihood ratio statistics \(\lambda (n)=\sup_{\theta \in \Theta}l_ n(\theta)-\sup_{\theta \in \Theta_ 0}l_ n(\theta)\) is considered. Let m, \(m_ 0\), a and \(c<a\) be given numbers and let \(T=\inf \{n:\) \(n\geq m_ 0\), \(\lambda (n)>a\}\). The repeated significance test (RST) rejects \(H_ 0\) if \(T\leq m\). The modified RST (MRST) rejects \(H_ 0\) if either \(T\leq m\) or \(T>m\) and \(\lambda (n)>c.\)
The power and significance level of RST and MRST are discussed in detail. Numerical and Monte Carlo results are presented.

Reviewer: R.Zielinski

MSC:

62L10	Sequential statistical analysis
62F03	Parametric hypothesis testing

Keywords:

sequence of log-likelihood ratio statistics; repeated significance test; power; significance level; Monte Carlo results