  In this paper, we have established a unified framework of multistage
parameter estimation. We demonstrate that a wide variety of statistical
problems such as fixed-sample-size interval estimation, point estimation with
error control, bounded-width confidence intervals, interval estimation
following hypothesis testing, construction of confidence sequences, can be cast
into the general framework of constructing sequential random intervals with
prescribed coverage probabilities. We have developed exact methods for the
construction of such sequential random intervals in the context of multistage
sampling. In particular, we have established inclusion principle and coverage
tuning techniques to control and adjust the coverage probabilities of
sequential random intervals. We have obtained concrete sampling schemes which
are unprecedentedly efficient in terms of sampling effort as compared to
existing procedures.
