Abstract: A hypothesis testing problem is considered where the distribution of a random sample is specified only up to a nuisance parameter. Under the notion of asymptotic efficiency according to Bahadur, an adaptive test statistic is asymptotically efficient regardless of the value of the nuisance parameter. An adaptation condition is derived and the form of adaptive test statistics is discussed.
Key words and phrases: Bahadur efficiency, adaptive test statistics, stochastic comparison of tests, attained level, exact slope, linear inequalities, likelihood ratio test.