Coverage probability

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

Frequentist evaluation of intervals estimated for a binomial parameter and for the ratio of Poisson means

Abstract: Confidence intervals for a binomial parameter or for the ratio of Poisson means are commonly desired in high energy physics (HEP) applications such as measuring a detection efficiency or branching ratio. Due to the discreteness of the data, in both of these problems the frequentist coverage probability unfortunately depends on the unknown parameter. Trade-offs among desiderata have led to numerous sets of intervals in the statistics literature, while in HEP one typically encounters only the classic intervals of Clopper–Pearson (central intervals with no undercoverage but substantial over-coverage) or a few approximate methods which perform rather poorly. If strict coverage is relaxed, some sort of averaging is needed to compare intervals. In most of the statistics literature, this averaging is over different values of the unknown parameter, which is conceptually problematic from the frequentist point of view in which the unknown parameter is typically fixed. In contrast, we perform an (unconditional) average over observed data in the ratio-of-Poisson-means problem. If strict conditional coverage is desired, we recommend Clopper–Pearson intervals and intervals from inverting the likelihood ratio test (for central and non-central intervals, respectively). Lancaster's mid- P modification to either provides excellent unconditional average coverage in the ratio-of-Poisson-means problem.

On the Energy-Efficient Deployment for Ultra-Dense Heterogeneous Networks With NLoS and LoS Transmissions

Abstract: We investigate network performance of ultra-dense heterogeneous networks and study the maximum energy-efficient base station deployment incorporating probabilistic non-line-of-sight and line-of-sight transmissions. First, we develop an analytical framework with the maximum instantaneous received power and the maximum average received power association schemes to model the coverage probability and related performance metrics, e.g., the potential throughput and the energy efficiency (EE). Second, we formulate two optimization problems to achieve the maximum energy-efficient deployment solution with specific service criteria. Simulation results show that there are tradeoffs among the coverage probability, the total power consumption, and the EE. To be specific, the maximum coverage probability with ideal power consumption is superior to that with practical power consumption when the total power constraint is small and inferior to that with practical power consumption when the total power constraint becomes large. Moreover, the maximum EE is a decreasing function with respect to the coverage probability constraint.

An alternative pseudolikelihood method for multivariate random-effects meta-analysis

Abstract: Recently, multivariate random-effects meta-analysis models have received a great deal of attention, despite its greater complexity compared to univariate meta-analyses. One of its advantages is its ability to account for the within-study and between-study correlations. However, the standard inference procedures, such as the maximum likelihood or maximum restricted likelihood inference, require the within-study correlations, which are usually unavailable. In addition, the standard inference procedures suffer from the problem of singular estimated covariance matrix. In this paper, we propose a pseudolikelihood method to overcome the aforementioned problems. The pseudolikelihood method does not require within-study correlations and is not prone to singular covariance matrix problem. In addition, it can properly estimate the covariance between pooled estimates for different outcomes, which enables valid inference on functions of pooled estimates, and can be applied to meta-analysis where some studies have outcomes missing completely at random. Simulation studies show that the pseudolikelihood method provides unbiased estimates for functions of pooled estimates, well-estimated standard errors, and confidence intervals with good coverage probability. Furthermore, the pseudolikelihood method is found to maintain high relative efficiency compared to that of the standard inferences with known within-study correlations. We illustrate the proposed method through three meta-analyses for comparison of prostate cancer treatment, for the association between paraoxonase 1 activities and coronary heart disease, and for the association between homocysteine level and coronary heart disease. © 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

A General Method of Determining Fixed-Width Confidence Intervals

Abstract: 0. Summary. A general method for determining stopping rules to obtain a fixed-width confidence interval of prescribed coverage probability for an unknown parameter of a distribution is obtained. Asymptotic theory in the sense of Chow and Robbins [4] is discussed. The sequential procedure obtained is asymptotically consistent and efficient in the sense of Chow and Robbins [4]. 1. Introduction. Fixed-width confidence interval estimation for the mean of a normal distribution has been considered by Ray [6] and Starr [7] etc. The analogous problem for the variance of a normal population has been considered by Graybill and Connell [5] by using two stage sampling. Chow and Robbins [4] have considered the problem of determining a confidence interval of prescribed width and prescribed coverage probability for the unknown mean of a population with unknown finite variance. They constructed a stopping rule and thereby developed an asymptotic theory in a certain sense. When there are some nuisance parameters present, presumbaly unknown, fixed sample size procedure will usually not work to obtain a fixed-width interval with a given coverage probability. But there are examples where there are no nuisance parameters and still the fixed sample size procedure does not work, e.g., for the variance of a normal population with zero mean. In all such cases a stopping rule can be adopted which will provide a bounded length confidence interval of given coverage probability. However, bounded length confidence intervals with prescribed coverage probability have been treated in few special cases. The object of this note is to give a general method of constructing sequential procedure for obtaining fixed-width confidence intervals of prescribed coverage probability for an unknown parameter of a distribution involving possibly some unknown nuisance parameters. The distribution involved will be assumed to be known except for the parameters. For the sake of simplicity, the discussion is restricted to the case of a single nuisance parameter since the case of several nuisance parameters is immediate. Let p (x, 01., 02) be the probability density function of a random variable X (for convenience with respect to Lebesque measure) with real valued parameters 01 and 02 where 02 is regarded as nuisance parameter. We want to determine a confidence interval of fixed-width 2d (d > 0) for 01 when both 01 and 02 are unknown, with preassigned coverage probability 1 - a (O < a < 1). ASSUMPTION. We assume that all the regularity assumptions of maximum likelihood estimation are satisfied.