Abstract

Abstract: When estimating the mean of a normal distribution with squared error loss and a cost for each observation, the optimal (fixed) sample size depends on the variance s2. A two-stage sequential procedure is to first conduct a pilot study from which s2 can be estimated, and then estimate the desired sample size. Here an asymptotic formula for the initial sample size in a twostage sequential estimation procedure is derived-asymptotic as the cost of a single observation becomes small compared to the loss from estimation error. The experimenter must specify only the sample size, no say, that would be used in a fixed sample size experiment; the initial sample size of the two-

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