In this paper, we have established a unified framework of multistage parametric estimation. We demonstrate that a wide spectrum of classical sequential problems such as point estimation with error control, bounded-width confidence intervals, interval estimation following hypothesis testing, construction of confidence sequences, can be cast in the general framework of random intervals. We have developed exact methods for the construction of such random intervals in the context of multistage sampling. Our sampling schemes are unprecedentedly efficient in terms of sampling effort as compared to existing sampling procedures.
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