Coverage probability

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

Time-simultaneous prediction band for a time series

Abstract: I propose principles and methods for the construction of a time-simultaneous prediction band for a univariate time series. The methods are entirely based on a learning sample of time trajectories, and make no parametric assumption about its distribution. Hence, the methods are general and widely applicable. The expected coverage probability of a band can be estimated by a bootstrap procedure. The estimate is likely to be less than the nominal level. Expected lack of coverage can be compensated for by increasing the coverage in the learning sample. Applications to simulated and empirical data illustrate the methods. Copyright © 2007 John Wiley & Sons, Ltd.

Estimation of an overall standardized mean difference in random-effects meta-analysis if the distribution of random effects departs from normal.

Abstract: The random-effects model, applied in most meta-analyses nowadays, typically assumes normality of the distribution of the effect parameters. The purpose of this study was to examine the performance of various random-effects methods (standard method, Hartung's method, profile likelihood method, and bootstrapping) for computing an average effect size estimate and a confidence interval (CI) around it, when the normality assumption is not met. For comparison purposes, we also included the fixed-effect model. We manipulated a wide range of conditions, including conditions with some degree of departure from the normality assumption, using Monte Carlo simulation. To simulate realistic scenarios, we chose the manipulated conditions from a systematic review of meta-analyses on the effectiveness of psychological treatments. We compared the performance of the different methods in terms of bias and mean squared error of the average effect estimators, empirical coverage probability and width of the CIs, and variability of the standard errors. Our results suggest that random-effects methods are largely robust to departures from normality, with Hartung's profile likelihood methods yielding the best performance under suboptimal conditions.

Unified Analysis of HetNets using Poisson Cluster Process under Max-Power Association

Abstract: Owing to its flexibility in modeling real-world spatial configurations of users and base stations (BSs), the Poisson cluster process (PCP) has recently emerged as an appealing way to model and analyze heterogeneous cellular networks (HetNets). Despite its undisputed relevance to HetNets -- corroborated by the models used in industry -- the PCP's use in performance analysis has been limited. This is primarily because of the lack of analytical tools to characterize performance metrics such as the coverage probability of a user connected to the strongest BS. In this paper, we develop an analytical framework for the evaluation of the coverage probability, or equivalently the complementary cumulative density function (CCDF) of signal-to-interference-and-noise-ratio (SINR), of a typical user in a K-tier HetNet under a max power-based association strategy, where the BS locations of each tier follow either a Poisson point process (PPP) or a PCP. The key enabling step involves conditioning on the parent PPPs of all the PCPs which allows us to express the coverage probability as a product of sum-product and probability generating functionals (PGFLs) of the parent PPPs. In addition to several useful insights, our analysis provides a rigorous way to study the impact of the cluster size on the SINR distribution, which was not possible using existing PPP-based models.

The empirical coverage of confidence intervals: point estimates and confidence intervals for confidence levels.

Abstract: Many confidence intervals calculated in practice are potentially not exact, either because the requirements for the interval estimator to be exact are known to be violated, or because the (exact) distribution of the data is unknown If a confidence interval is approximate, the crucial question is how well its true coverage probability approximates its intended coverage probability In this paper we propose to use the bootstrap to calculate an empirical estimate for the (true) coverage probability of a confidence interval In the first instance, the empirical coverage can be used to assess whether a given type of confidence interval is adequate for the data at hand More generally, when planning the statistical analysis of future trials based on existing data pools, the empirical coverage can be used to study the coverage properties of confidence intervals as a function of type of data, sample size, and analysis scale, and thus inform the statistical analysis plan for the future trial In this sense, the paper proposes an alternative to the problematic pretest of the data for normality, followed by selection of the analysis method based on the results of the pretest We apply the methodology to a data pool of bioequivalence studies, and in the selection of covariance patterns for repeated measures data

Coverage Probability and Achievable Rate Analysis of FFR-Aided Multi-User OFDM-Based MIMO and SIMO Systems

Abstract: Expressions are derived for the coverage probability and average rate of both multi-user multiple input multiple output (MU-MIMO) and single input multiple output (SIMO) systems in the context of a fractional frequency reuse (FFR) scheme. In particular, given a reuse region of $\frac{1}{3}$ (FR3) and a reuse region of 1 (FR1) as well as a signal-to-interference-plus-noise-ratio (SINR) threshold $S_{th}$ , which decides the user assignment to either the FR1 or FR3 regions, we theoretically show that: $1)$ the optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$ , where $T$ is the target SINR required for ensuring adequate coverage, and $2)$ the optimal choice of $S_{th}$ which maximizes the average rate is given by $S_{th}= T^{\prime}$ , where $T^{\prime}$ is a function of the path loss exponent, the number of antennas and of the fading parameters. The impact of frequency domain correlation amongst the OFDM sub-bands allocated to the FR1 and FR3 cell-regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the FFR network. Furthermore, the performance of our FFR-aided MU-MIMO and SIMO systems is compared. Our analysis shows that the (2 $\times$ 2) MU-MIMO system achieves 22.5% higher rate than the (1 $\times$ 3) SIMO system and for lower target SINRs, the coverage probability of a (2 $\times$ 2) MU-MIMO system is comparable to a (1 $\times$ 3) SIMO system. Hence the former one may be preferred over the latter. Our simulation results closely match the analytical results.