Coverage probability

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

Conditional Validity of Inductive Conformal Predictors

Abstract: Conformal predictors are set predictors that are automatically valid in the sense of having coverage probability equal to or exceeding a given confidence level. Inductive conformal predictors are a computationally efficient version of conformal predictors satisfying the same property of validity. However, inductive conformal predictors have only been known to control unconditional coverage probability. This paper explores various versions of conditional validity and various ways to achieve them using inductive conformal predictors and their modifications. In particular, it discusses a convenient expression of one of the modifications in terms of ROC curves.

Kappa statistic for clustered matched‐pair data

Abstract: Kappa statistic is widely used to assess the agreement between two procedures in the independent matched-pair data. For matched-pair data collected in clusters, on the basis of the delta method and sampling techniques, we propose a nonparametric variance estimator for the kappa statistic without within-cluster correlation structure or distributional assumptions. The results of an extensive Monte Carlo simulation study demonstrate that the proposed kappa statistic provides consistent estimation and the proposed variance estimator behaves reasonably well for at least a moderately large number of clusters (e.g., K ⩾50). Compared with the variance estimator ignoring dependence within a cluster, the proposed variance estimator performs better in maintaining the nominal coverage probability when the intra-cluster correlation is fair (ρ ⩾0.3), with more pronounced improvement when ρ is further increased. To illustrate the practical application of the proposed estimator, we analyze two real data examples of clustered matched-pair data. Copyright © 2014 John Wiley & Sons, Ltd.

Simultaneous confidence intervals for ratios with applications to the comparison of several treatments with a control.

Abstract: Objectives: In this article, we illustrate and compare exact simultaneous confidence sets with various approximate simultaneous confidence intervals for multiple ratios as applied to many-to-one comparisons Quite different datasets are analyzed to clarify the points Methods: The methods are based on existing probability inequalities (eg, Bonferroni, Slepian and Sidak), estimation of nuisance parameters and re-sampling techniques Exact simultaneous confidence sets based on the multivariate t -distribution are constructed and compared with approximate simultaneous confidence intervals Results: It is found that the coverage probabilities associated with the various methods of constructing simultaneous confidence intervals (for ratios) in manyto- one comparisons depend on the ratios of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments If the ratios of the coefficients of variations are less than one, the Bonferroni corrected Fieller confidence intervals have almost the same coverage probability as the exact simultaneous confidence sets Otherwise, the use of Bonferroni intervals leads to conservative results Conclusions: When the ratio of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments are greater than one (eg, in balanced designs with increasing effects), the Bonferroni simultaneous confidence intervals are too conservative Therefore, we recommend not using Bonferroni for this kind of data On the other hand, the plug-in method maintains the intended confidence coefficient quite satisfactorily; therefore, it can serve as the best alternative in any case

Asymptotic Behavior of a Class of Confidence Regions Based on Ranks in Regression

Abstract: Asymptotic behavior of a class of confidence regions, based on rank statistics, for the regression parameter vector is considered. These regions are shown to be asymptotically bounded and ellipsoidic in probability. Asymptotic normality of their center of gravities is also proved. It is noted that the asymptotic efficiencies of these regions when defined in terms of ratio of Lebesgue measures corresponds to that of corresponding test statistics that are used to define these regions. Similar conclusion holds for their center of gravities, where now asymptotic efficiency is defined as inverse ratio of their generalized limiting variances. Also a class of consistent estimators is given for some functionals of the underlying distributions. Finally simultaneous confidence intervals, based on the above center of gravity, for linear parametric functions are shown to have asymptotic coverage probability $1 - \alpha$. Basic to this work are two papers, one by the author [4] and one by Jureckova [3].

Relative width sequential confidence intervals for the mean

Abstract: In this paper we discuss two sequential procedures for constructing confidence intervals for the mean with a relative width requirement. Carefully stating the procedure proposed by Nadas and the procedure considered by Thomas, Iglehart, Robinson, Lavenberg and Sauer, and Law, we give some efficiency and consistency results concerning the latter, and compare their small-sample performances on a variety of stochastic models for which analytic results are available.