Topic
Coverage probability
About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.
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TL;DR: In this paper, the authors considered the problem of constructing confidence sets for the structural errors-in-variables model under the assumption that the variance of the error associated with the covariate is known.
Abstract: The problem of constructing confidence sets for the structural errors-in-variables model is considered under the assumption that the variance of the error associated with the covariate is known. Previously proposed confidence sets for this model suffer from the problem that they all have zero confidence levels for any sample size, where the confidence level of a confidence set is defined to be the infimum of coverage probability over the parameter space. In this paper we construct some asymptotically honest confidence sets; that is, the limiting values of their confidence levels are at least as large as the nominal probabilities when the sample size goes to $\infty$. A desirable property of the proposed confidence set for the slope is also established.
11 citations
TL;DR: The solution presented can be uniformly adopted and from the RMSE point of view, REML accounting for heterogeneity outperforms REML assuming homogeneity; a considerable improvement has been particularly detected for the fixed parameters.
Abstract: This article uses Monte Carlo techniques to examine the effect of heterogeneity of variance in multilevel analyses in terms of relative bias, coverage probability, and root mean square error (RMSE). For all simulated data sets, the parameters were estimated using the restricted maximum-likelihood (REML) method both assuming homogeneity and incorporating heterogeneity into multilevel models. We find that (a) the estimates for the fixed parameters are unbiased, but the associated standard errors are frequently biased when heterogeneity is ignored; by contrast, the standard errors of the fixed effects are almost always accurate when heterogeneity is considered; (b) the estimates for the random parameters are slightly overestimated; (c) both the homogeneous and heterogeneous models produce standard errors of the variance component estimates that are underestimated; however, taking heterogeneity into account, the REML-estimations give correct estimates of the standard errors at the lowest level and lead to less underestimated standard errors at the highest level; and (d) from the RMSE point of view, REML accounting for heterogeneity outperforms REML assuming homogeneity; a considerable improvement has been particularly detected for the fixed parameters. Based on this, we conclude that the solution presented can be uniformly adopted. We illustrate the process using a real dataset.
11 citations
TL;DR: It is shown that bootstrap confidence intervals for the value of the ROC curve at a fixed false positive fraction based on the new estimate are on average shorter compared to the approach by Zhou and Qin (2005, while maintaining coverage probability), and the estimator is quite robust against modest deviations from the log-concavity assumption.
Abstract: We introduce a new smooth estimator of the ROC curve based on log-concave density estimates of the constituent distributions. We show that our estimate is asymptotically equivalent to the empirical ROC curve if the underlying densities are in fact log-concave. In addition, we empirically show that our proposed estimator exhibits an efficiency gain for finite sample sizes with respect to the standard empirical estimate in various scenarios and that it is only slightly less efficient, if at all, compared to the fully parametric binormal estimate in case the underlying distributions are normal. The estimator is also quite robust against modest deviations from the logconcavity assumption. We show that bootstrap confidence intervals for the value of the ROC curve at a fixed false positive fraction based on the new estimate are on average shorter compared to the approach by Zhou and Qin (2005), while maintaining coverage probability. Computation of our proposed estimate uses the R package logcondens that implements univariate log-concave density estimation and can be done very efficiently using only one line of code. These obtained results lead us to advocate our estimate for a wide range of scenarios.
11 citations
01 Jan 2001
TL;DR: A simulation study shows that the bootstrap-t gives better coverage probability, but is considerably more computer-intensive than non-bias-corrected versions, which leads to the development of an importance resampling technique which can reduce the CPU time by a factor of 10 or more.
Abstract: We start with a data set recently obtained from a Bruceton test. The data come from the study of CS-M-3 ignitor in a military experiment and are analyzed by the up-and-down method of Dixon and Mood (1948). We reexamine the method and develop a more appropriate inference that takes account of the special dependent data structure. Two bootstrap confidence interval procedures, percentile and bootstrap-t, are introduced to find approximate confidence intervals for the parameters of interest. A simulation study shows that the bootstrap-t ,w ith proper bias corrections, gives better coverage probability, but is considerably more computer-intensive than non-bias-corrected versions. This leads to the development of an importance resampling technique which can reduce the CPU time by a factor of 10 or more. Finally, we apply the proposed procedure to analyze our data set.
11 citations
TL;DR: It was found that if the publication bias is not adjusted it could lead to up to 40% biased in treatment effect estimates if the data was incorrectly adjusted, and coverage probability for estimates based on this incorrectly adjusted data is not significantly different from those of which is correctly not adjusted.
Abstract: Publication bias in meta-analysis is a serious issue as it may lead to biased estimates which appear to be precise. A popular method for detecting and adjusting the publication bias is the trim and fill method. This study uses simulated meta-analysis to quantify the effects of publication bias on the overall meta-analysis estimates of continuous data where the absolute mean difference was utilized as the measure of effect. It additionally evaluates the performance of the trim and fills method for adjusting the publication bias in terms of statistical bias, the standard errors and the coverage probability. The results demonstrate that if the publication bias is not adjusted it could lead to up to 40% biased in treatment effect estimates. Utilization of the trim and fill method has reduced the bias in the overall effect estimate by more than half. It is optimum in presence of moderate underlying bias but has minimal effects in presence of low and severe bias. Additionally, the trim and fill method improves the coverage probability by more than half when subjected to the same level of publication bias as those of the unadjusted data. However, the method tends to produce false positive results. A sensitivity analysis suggests that the trim and fill method will incorrectly adjust the data for publication bias between 10-45% of the time (for the 5% nominal level). Although the data was incorrectly adjusted, it was found that the Percentage Relative Bias (PRB) introduced into the estimates due to this adjustment is minimal (min: 0.007%, max: 0.109%) and coverage probability for estimates based on this incorrectly adjusted data is not significantly different from those of which is correctly not adjusted. Therefore the trim and fill method is recommended be routinely used when conducting meta-analysis.
11 citations