Coverage probability

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

Accurate Multivariate Estimation Using Triple Sampling

Abstract: Any multiresponse estimation experiment requires a decision about the number of observations to be taken. If the covariance is unknown, no fixed-sample-size procedure can guarantee that the joint confidence region will have an assigned shape and level. Double-sampling procedures use a preliminary sample of size $m$ to determine the minimum number of additional observations needed to achieve a prescribed accuracy and coverage probability for the parameter estimates. The triple-sampling procedures of this paper, less sensitive to the choice of $m$, revise the sample size estimate after collecting a fraction of the additional observations prescribed under double sampling. Second-order asymptotic results relying on conditional inference show that triple sampling is asymptotically consistent; in addition, the regret for triple sampling is a bounded function of the covariance structure and is independent of $m$.

Summarizing the output of a Monte Carlo method for uncertainty evaluation

Abstract: The ?Guide to the Expression of Uncertainty in Measurement? (GUM) requires that the way a measurement uncertainty is expressed should be transferable. It should be possible to use directly the uncertainty evaluated for one measurement as a component in evaluating the uncertainty for another measurement that depends on the first. Although the method for uncertainty evaluation described in the GUM meets this requirement of transferability, it is less clear how this requirement is to be achieved when GUM Supplement 1 is applied. That Supplement uses a Monte Carlo method to provide a sample composed of many values drawn randomly from the probability distribution for the measurand. Such a sample does not constitute a convenient way of communicating knowledge about the measurand. In this paper consideration is given to obtaining a more compact summary of such a sample that preserves information about the measurand contained in the sample and can be used in a subsequent uncertainty evaluation. In particular, a coverage interval for the measurand that corresponds to a given coverage probability is often required. If the measurand is characterized by a probability distribution that is not close to being Gaussian, sufficient information has to be conveyed to enable such a coverage interval to be computed reliably.A quantile function in the form of an extended lambda distribution can provide adequate approximations in a number of cases. This distribution is defined by a fixed number of adjustable parameters determined, for example, by matching the moments of the distribution to those calculated in terms of the sample of values. In this paper, alternative flexible models for the quantile function and methods for determining a quantile function from a sample of values are proposed for meeting the above needs.

Closed Form Prediction Intervals Applied for Disease Counts

Abstract: The prediction interval is an important tool in medical applications for predicting the number of times a disease will occur in a population. The performance of the existing prediction intervals, however, is unsatisfactory when the true proportion is near a boundary. Since the true proportion can be very small in real applications, in this article, we propose improved prediction intervals with better coverage probability than the existing methods. Their predictive distributions are compared in terms of the Kullback–Leibler distance and the intervals are compared using a hearing screening medical example.

Confidence interval calculation for a sequential clinical trial of binary responses

Abstract: Consider a sequential test applied to two streams of binary responses in a comparative clinical trial. After the completion of such a trial Woodroofe's (1992) technique for accurate confidence interval estimation for a treatment difference can be applied. In this paper the technique is extended to provide confidence intervals for the individual absolute success probabilities of the two treatments in the trial, for which no current methodology exists. Accuracy is explored by simulation of coverage probabilities and individual confidence limit probabilities. The simulations concern a triangular test and an O'Brien & Fleming test.