On a class of purely sequential procedures with applications to estimation and ranking and selection problems

In this article, we develop a general class of purely sequential procedures and obtain the associated first- and second-order asymptotics for the expected sample size and regret. We establish that many estimation and ranking and selection problems can be handled with the help of the proposed class of sequential procedures. A brief simulation analysis is carried out in support of the accuracy of our proposed sequential methodology and a real data set from environment study is included to demonstrate the practical utility.