I Sequential Sampling

Most statistical techniques are based on a sample of fixed sizen. This may be becausenis chosen beforehand or because it is dictated by the circumstances. Sometimes, however, the members of the sample occur one after the other and we can then use sequential methods. A sequential sampling scheme gives us a ‘stopping rule’ for deciding, after observing each successive member of the sample, whether we can stop sampling and reach a decision or whether we must examine another member. As an example take the problem of deciding between hypotheses H0and H1that a parameterθtakes one of two valuesθ0andθ1respectively, using Wald's Sequential Probability Ratio (SPR) test.