Sequential Hypothesis Testing

Abstract

Sequential sampling is a fast efficient tool for many sampling problems. Sequential sampling may be used (1) to obtain precise estimate(s) of the parameters), or (2) to test hypotheses concerning the parameters. Sequential estimation is used when the purpose of sampling is to obtain precise parameter estimates. Several sequential estimation procedures are discussed in Chapter 4. The focus of this chapter is sequential hypothesis testing. This approach is appropriate when we are interested in determining whether the population density is above or below a stated threshold. As in sequential estimation, sequential hypothesis testing requires taking observations sequentially until some stopping criterion is satisfied. The observations are taken at random over the sampling area. Generally, the accumulated total of the observations relative to the number of observations taken determines when sampling is stopped. The sequential hypothesis testing we consider requires some prior knowledge of the population distribution. This permits most computations to be completed in advance of sampling and to be stored in handheld calculators, laptop computers, or printed on cards or sheets. Wald’s sequential probability ratio test was the earliest sequential test and is described first. Lorden’s 2-SPRT is a more recent development that has some exciting possibilities for tests of hypotheses concerning population density and is discussed in the latter parts of this chapter.