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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: The authors generalize the PoSI intervals to post-model-selection predictors, and apply them to linear regression models with pre-model selection and postmodel selection in linear regression.
Abstract: We consider inference post-model-selection in linear regression. In this setting, Berk et al.(2013) recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain non-standard quantity of interest with a user-specified minimal coverage probability, irrespective of the model selection procedure that is being used. In this paper, we generalize the PoSI intervals to post-model-selection predictors.
12 citations
TL;DR: Five methods are compared and contrasted for performing the intermediate step of fine mapping to isolate disease loci to narrow intervals with high confidence so that association studies can be more focused, efficient, and cost‐effective.
Abstract: The arrival of highly dense genetic maps at low cost has geared the focus of linkage analysis studies toward developing methods for placing putative trait loci in narrow regions with high confidence. This shift has led to a new analytic scheme that expands the traditional two-stage protocol of preliminary genome scan followed by fine mapping through inserting a new stage in between the two. The goal of this new "intermediate" fine mapping stage is to isolate disease loci to narrow intervals with high confidence so that association studies can be more focused, efficient, and cost-effective. In this paper, we compared and contrasted five methods that can be used for performing this intermediate step. These methods are: the lod support approach, the generalized estimating equations (GEE) method, the confidence set inference (CSI) procedure, and two bootstrap methods. We compared these methods in terms of the coverage probability and precision of localization of the resulting intervals. Results from a simulation study considering several two-locus models demonstrated that the two bootstrap methods yield intervals with approximately correct coverage. On the other hand, the 1-lod support intervals, and those produced by the GEE method, tend to significantly undercover the trait locus, while the regions obtained by the CSI incline to overcover the gene position. When the observed coverage of the confidence intervals produced by all the methods was held to be the same, those obtained through the CSI procedure displayed a higher ability to localize loci, especially when these loci have a minor contribution to the trait and when the amount of data available for the analysis is relatively small. However, with very large sample sizes, lod support intervals emerged as a winner. Application of the methods to the data from the Arthritis Research Campaign National Repository led to intervals containing the position of a known trait locus for all methods, with the greatest precision achieved by the CSI.
12 citations
TL;DR: Simulation results indicate that the proposed approximate confidence intervals perform reasonably well when the standard deviation of the log-transformed variable is small.
Abstract: In this work, approximate confidence intervals are derived for the standard deviation of a log-normal distribution. Simulations are conducted to evaluate the coverage probability, average length, and coverage bias of the derived approximate confidence intervals. The simulation results indicate that the proposed approximate confidence intervals perform reasonably well when the standard deviation of the log-transformed variable is small. The approximate confidence intervals are applied to a phase I pharmacokinetic study and a real data set concerning a lab testing of reference engine oil. Copyright © 2015 John Wiley & Sons, Ltd.
12 citations
TL;DR: Estimations to the moments, different possibilities for the limiting distributions and approximate confidence intervals for the maximum-likelihood estimator of a given parametric function when sampling from partially non-regular log-exponential models and Pareto distribution are proposed.
Abstract: We propose approximations to the moments, different possibilities for the limiting distributions and approximate confidence intervals for the maximum-likelihood estimator of a given parametric function when sampling from partially non-regular log-exponential models. Our results are applicable to the two-parameter exponential, power-function and Pareto distribution. Asymptotic confidence intervals for quartiles in several Pareto models have been simulated. These are compared to asymptotic intervals based on sample quartiles. Our intervals are superior since we get shorter intervals with similar coverage probability. This superiority is even assessed probabilistically. Applications to real data are included.
12 citations
TL;DR: Wang et al. as mentioned in this paper proposed a B-spline quantile regression probability density prediction method to predict future runoff and quantify the uncertainty of prediction, which is applicable to the Shigu station of the Jinsha River in China.
12 citations