PRINCIPLES OF OPTIMAL SEQUENTIAL PLANNING Claudia Schmegner 1 and Michael I. Baron 2 1 Department of Mathematical Sciences, DePaul University, Chicago, IL 60614 2 Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083-0688, IBM Research Division, Yorktown Heights, NY 10598 ABSTRACT A concept of sequential planning is presented as extension and generalization of “pure” sequential procedures. According to it, observations are collected in groups of variable sizes. The article discusses optimality of sequential plans in terms of a suitable risk function that balances an observation cost and a group cost. It is shown that only non-randomized sequential plans based on a sufficient statistic need to be considered in order to achieve optimality. Performance of several classes of plans is evaluated. Key words and Phrases: cost, risk, sequential plan, sequentially planned probability ratio test 1. INTRODUCTION The main principle of classical sequential sampling is to collect one obser- vation at a time. After each observation is collected, the experimenter decides whether to make a decision immediately (and stop data collection) or to post- 1