7.2 The stopping rule principle

7.2.1 Definitions

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

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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 ...

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