Nearly optimal sequential tests of composite hypotheses. (English) Zbl 0657.62088

Lai, Tze Leung

Ann. Stat. 16, No. 2, 856-886 (1988).

A unified approach to testing \(H_ 0:\) \(\theta \leq \theta_ 0\) vs \(H_ 1:\) \(\theta \geq \theta_ 1\) and H: \(\theta <\theta_ 0\) vs K: \(\theta >\theta_ 0\) in exponential families with pdf’s exp(\(\theta\) x-\(\psi\) (\(\theta)\)) is presented. A new class of sequential tests is proposed. Asymptotic optimality, as the sampling cost tends to zero, is discussed.

Reviewer: R.Zielinski

MSC:

62L10	Sequential statistical analysis
62L05	Sequential statistical design
62L15	Optimal stopping in statistics

Keywords:

Bayes sequential tests; diffusion approximations; Kullback-Leibler information; generalized sequential likelihood ratio tests; boundary crossing probabilities; exponential families; Asymptotic optimality