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In this paper, we have established a general framework of multistage hypothesis tests which applies to arbitrarily many mutually exclusive and exhaustive composite hypotheses. Within the new framework, we have constructed specific multistage tests which rigorously control the risk of committing decision errors and are more efficient than previous tests in terms of average sample number and the number of sampling operations. Without truncation, the sample numbers of our testing plans are absolutely bounded.
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 co
In this paper, we have developed new multistage tests which guarantee prescribed level of power and are more efficient than previous tests in terms of average sampling number and the number of sampling operations. Without truncation, the maximum samp
In this article, we derive a new generalization of Chebyshev inequality for random vectors. We demonstrate that the new generalization is much less conservative than the classical generalization.
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In pa
We introduce a general method, named the h-function method, to unify the constructions of level-alpha exact test and 1-alpha exact confidence interval. Using this method, any confidence interval is improved as follows: i) an approximate interval, inc