Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.

Assessing accuracy in linkage analysis by means of confidence regions

Abstract: When statistical linkage to a certain chromosomal region has been found, it is of interest to develop methods which quantify the accuracy with which the disease locus can be mapped. In this paper, we investigate the performance of three different types of confidence regions with asymptotically correct coverage probability as the number of pedigrees grows. Our setup is that of a saturated map of marker data. We show that the expected length of the confidence region is inversely proportional to the square of the noncentrality parameter and to a certain normalized slope-to-noise ratio. Our investigations reveal that testing performance criteria (such as the power to detect linkage) can be quite different from estimation based performance criteria (such as the expected length of a confidence region).

An improved confidence ellipsoid for the linear regression model

Abstract: In a Monte Carlo experiment, we explore the coverage probability and volume of a percentile bootstrap confidence ellipsoid centered at the Stein-rule estimator of a multivariate normal mean. The ellipsoid we consider corresponds to the “improved-F” studied by Ullah, Carter, and Srivastava (1984, 1989) who have derived the small sigma and large-T asymptotic expansions of its distribution and studied the resulting approximations in a Monte Carlo setting. Unlike the Ullah et al. ellipsoid, the bootstrap ellipsoid covers the parameter point at or above nominal levels over large regions of the parameter space.

Robustness of sample size re-estimation procedure in clinical trials (arbitrary populations).

Abstract: In clinical trials, one of the main questions that is being asked is how many additional observations, if any, are needed beyond those originally planned. In a two-treatment double-blind clinical experiment, one is interested in testing the null hypothesis of equality of the means against one-sided alternative when the common variance sigma2 is unknown. We wish to determine the required total sample size when the error probabilities alpha and beta are specified at a predetermined alternative. Shih provided a two-stage procedure which is an extension of Stein's one-sample procedure, assuming normal response. He estimates sigma2 by the method of maximum likelihood via the EM algorithm and carries out a simulation study in order to evaluate the effective level of significance and the power. The author proposed a closed-form estimator for sigma2 and showed analytically that the difference between the effective and nominal levels of significance is negligible and that the power exceeds 1-beta when the initial sample size is large. Here we consider responses from arbitrary distributions in which the mean and the variance are not functionally related and show that when the initial sample size is large, the conclusions drawn previously by the author still hold. The effective coverage probability of a fixed-width interval is also evaluated. Proofs of certain assertions are deferred to the Appendix.