Repeated significance tests for exponential families (Q1116247)

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.