Mathematics – Statistics Theory
Scientific paper
2008-09-08
Mathematics
Statistics Theory
247 pages, no figure; added more applications; main results appeared in Proceedings of SPIE, Orlando, Florida, USA, April 2010
Scientific paper
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.
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Duncan
This paper opens a new direction of computational statistics.
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