Sequential point estimation of the mean when the distribution is unspecified

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Abstract
Two problems have been discussed in this paper. First, for independent and identically distributed random variables with unknown mean and unknown variance, a sequential procedure is proposed for point estimation of themean when the distribution is unspecified. Second, a sequential procedure is proposed for estimating the difference of the means of two populations when the variances are unknown (and not necessarily equal). The loss structure for both the problems is the cost of observations plus the squared error loss due to estimating theunknown mean or the difference of means. Without any assumption on the nature of the distribution functions other than the finiteness of the eighth moment, the two procedures are shown to be “asymptotically risk efficient” in the sense of Starr (Ann. Math. Statist. (1966), .37, 1173-1185).

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