Abstract
We develop a frequentist theory of estimation for the following problem. A statistician is given a sample by successive sampling from a large finite population. Units are listed in the order in which they were observed. With each sampled unit is provided one or more characteristics and the size measure which was used in drawing the successive sample. Based solely on the sample information and with no other information about the sampling frame, the statistician is to estimate population totals for the characteristics of interest. The problem arises in the literature of oil and gas forecasting and of reliability growth.
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