Sequential Estimation

Abstract
Summary: The literature on sequential estimation is reviewed, with special reference to inverse binomial sampling, double sampling, and asymptotic theory. An approximate distribution for the sample size is found for a certain type of sequential sampling rule, in which a cumulative sum of independent random variables all having the same continuous distribution is plotted against their number until a fixed boundary is first reached or crossed. Approximate methods are given for solving a number of particular problems, including (i) estimating the mean of a normal population by a confidence interval of prescribed width and coefficient, when the population variance is unknown, and (ii) estimating the parameters of a simple birth-death process so that the difference between the birth rate and the death rate is estimated with prescribed standard error. The possible usefulness of sequential estimation procedures is discussed.

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