Showing papers on "Coverage probability published in 1982"
TL;DR: For the problem of estimating a $p$-variate normal mean, the existence of confidence procedures which dominate the usual one, a sphere centered at the observations, has long been known, but no explicit procedure has yet been shown to dominate as discussed by the authors.
Abstract: For the problem of estimating a $p$-variate normal mean, the existence of confidence procedures which dominate the usual one, a sphere centered at the observations, has long been known. However, no explicit procedure has yet been shown to dominate. For $p \geq 4$, we prove that if the usual confidence sphere is recentered at the positive-part James Stein estimator, then the resulting confidence set has uniformly higher coverage probability, and hence is a minimax confidence set. Moreover, the increase in coverage probability can be quite substantial. Numerical evidence is presented to support this claim.
93 citations
TL;DR: In this paper, confidence intervals of prescribed width for the lo-cation parameter of an exponential distribution are obtained for the coverage probability and expected sample size, from which an asymptotic expression for the variance of the sample size is deduced.
Abstract: We study confidence intervals of prescribed width for the lo-cation parameter of an exponential distribution. Asymptotic expan-sions up to terms tending to zero are obtained for the coverage probability and expected sample size. The limiting distribution of the sample size is given from which an asymptotic expression for the variance of the sample size is deduced. Sequential procedures with non-asymptotic coverage probability are also investigated
41 citations
01 Jan 1982
TL;DR: In this article, an estimation-oriented confidence interval (CI) has been derived for the fixed sample size problems, which is superior to the test-oriented CI in most points of the parameter space.
Abstract: Publisher Summary In fixed sample size problems, there is a standard method for constructing a confidence set (CS) for a parameter θ with prescribed coverage probability 1– α. It employs a family of level a tests, with acceptance regions A(θ), and converts this into a CS by including in the CS all θ for which the observable random variable X lies in A(θ). This method is valid just as well in sequential situations. However, the sequential CSs that have appeared in the literature generally have not been derived this way. Rather, the approach has been to choose a sensible stopping rule and proposing a terminal decision rule consisting of a CS of desired shape. These two approaches to the construction of sequential CSs are termed test-oriented and estimation-oriented, respectively. This chapter discusses the estimation-oriented approach and shows that there is an estimation-oriented confidence intervals (CI) having the desired characteristics. In terms of sample size behavior, this CI is superior to the test-oriented CI's in most points of the parameter space.
9 citations