7.2 The stopping rule principle
We shall restrict ourselves to a simple situation, but it is possible to generalize the following account considerably; see Berger and Wolpert (1988, Section 4.2). Basically, in this section, we will consider a sequence of experiments which can be terminated at any stage in accordance with a rule devised by the experimenter (or forced upon him).
Suppose that the observations are independently and identically distributed with density and let
We say that s is a stopping rule or a stopping time if it is a random variable whose values are finite natural numbers with probability one, and is such that whether or not s> m depends solely on . In a sequential experiment E we observe the values where s is such a stopping rule and then stop. The restriction on the distribution of s means simply that whether or not you decide to stop cannot depend ...