Coverage probability

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

Frequentist prediction intervals and predictive distributions

Abstract: SUMMARY We consider parametric frameworks for the prediction of future values of a random variable Y, based on previously observed data X. Simple pivotal methods for obtaining calibrated prediction intervals are presented and illustrated. Frequentist predictive distri butions are defined as confidence distributions, and their utility is demonstrated. A simple pivotal-based approach that produces prediction intervals and predictive distributions with well-calibrated frequentist probability interpretations is introduced, and efficient simulation methods for producing predictive distributions are considered. Properties related to an average Kullback-Leibler measure of goodness for predictive or estimated distributions are given. The predictive distributions here are shown to be optimal in certain settings with invariance structure, and to dominate plug-in distributions under certain conditions.

Measuring inter-rater reliability for nominal data - which coefficients and confidence intervals are appropriate?

Abstract: Reliability of measurements is a prerequisite of medical research. For nominal data, Fleiss’ kappa (in the following labelled as Fleiss’ K) and Krippendorff’s alpha provide the highest flexibility of the available reliability measures with respect to number of raters and categories. Our aim was to investigate which measures and which confidence intervals provide the best statistical properties for the assessment of inter-rater reliability in different situations. We performed a large simulation study to investigate the precision of the estimates for Fleiss’ K and Krippendorff’s alpha and to determine the empirical coverage probability of the corresponding confidence intervals (asymptotic for Fleiss’ K and bootstrap for both measures). Furthermore, we compared measures and confidence intervals in a real world case study. Point estimates of Fleiss’ K and Krippendorff’s alpha did not differ from each other in all scenarios. In the case of missing data (completely at random), Krippendorff’s alpha provided stable estimates, while the complete case analysis approach for Fleiss’ K led to biased estimates. For shifted null hypotheses, the coverage probability of the asymptotic confidence interval for Fleiss’ K was low, while the bootstrap confidence intervals for both measures provided a coverage probability close to the theoretical one. Fleiss’ K and Krippendorff’s alpha with bootstrap confidence intervals are equally suitable for the analysis of reliability of complete nominal data. The asymptotic confidence interval for Fleiss’ K should not be used. In the case of missing data or data or higher than nominal order, Krippendorff’s alpha is recommended. Together with this article, we provide an R-script for calculating Fleiss’ K and Krippendorff’s alpha and their corresponding bootstrap confidence intervals.

Uniform Inference in Autoregressive Models

Abstract: The purpose of this paper is to provide theoretical justification for some existing methods for constructing confidence intervals for the sum of coefficients in autoregressive models. We show that the methods of Stock (1991), Andrews (1993), and Hansen (1999) provide asymptotically valid confidence intervals, whereas the subsampling method of Romano and Wolf (2001) does not. In addition, we generalize the three valid methods to a larger class of statistics. We also clarify the difference between uniform and pointwise asymptotic approximations, and show that a pointwise convergence of coverage probabilities for all values of the parameter does not guarantee the validity of the confidence set.

Simultaneous Confidence Intervals and Sample Size Determination for Multinomial Proportions

Abstract: Simultaneous confidence interval procedures for multinomial proportions are used in many areas of science. In this article two new simultaneous confidence interval procedures are introduced. Numerical results are presented to evaluate these procedures and compare their performance with established methods that have been used in statistical literature. From the results presented in this article, it is evident that the new procedures are more accurate than the established ones, where the accuracy of the procedure is measured by the volume of the confidence region corresponding to the nominal coverage probability and the probability of coverage it achieves. In the sample size determination problem, the new procedures provide a sizable amount of savings as compared to the procedures that have been used in many applications. Because both procedures performed equally well, the procedure that requires the least amount of computing time is recommended.

Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set

Abstract: This paper introduces a novel bootstrap procedure to perform inference in a wide class of partially identi…ed econometric models. We consider econometric models de…ned by …nitely many weak moment inequalities y , which encompass many applications of economic interest. The objective of our inferential procedure is to cover the identi…ed set with a prespeci…ed probability z . We compare our bootstrap procedure, a competing asymptotic approximation and subsampling proce- dures in terms of the rate at which they achieve the desired coverage level, also known as the error in the coverage probability. Under certain conditions, we show that our bootstrap procedure and the asymp- totic approximation have the same order of error in the coverage probability, which is smaller than the one obtained by using subsampling. This implies that inference based on our bootstrap and asymptotic approximation should eventually be more precise than inference based on subsampling. A Monte Carlo study con…rms this …nding in a small sample simulation.