On empirical Bayes testing with sequential components. (English) Zbl 0725.62011

Karunamuni, Rohana J.

Ann. Stat. 16, No. 3, 1270-1282 (1988).

Summary: We study the empirical Bayes decision theory with an m-truncated sequential statistical decision problem as the component. An empirical Bayes sequential decision procedure is constructed for the linear loss two-action problem. Asymptotic results are presented regarding the convergence of the Bayes risk of the empirical Bayes sequential decision procedure. With sequential components, an empirical Bayes sequential decision procedure selects both a stopping rule function and a terminal decision rule function for use in the component with parameter \(\theta\).

MSC:

62C12	Empirical decision procedures; empirical Bayes procedures
62L10	Sequential statistical analysis
62H15	Hypothesis testing in multivariate analysis

Keywords:

asymptotic optimality; asymptotic superiority; m-truncated sequential statistical decision; empirical Bayes sequential decision; linear loss two-action problem; convergence of the Bayes risk; stopping rule function; terminal decision rule function