False coverage rate

In statistics, a false coverage rate (FCR) is the average rate of false coverage, i.e. not covering the true parameters, among the selected intervals. The FCR gives a simultaneous coverage at a (1 − α)×100% level for all of the parameters considered in the problem. The FCR has a strong connection to the false discovery rate (FDR). Both methods address the problem of multiple comparisons, FCR from confidence intervals (CIs) and FDR from P-value's point of view. FCR was needed because of dangers caused by selective inference. Researchers and scientists tend to report or highlight only the portion of data that is considered significant without clearly indicating the various hypothesis that were considered. It is therefore necessary to understand how the data is falsely covered. There are many FCR procedures which can be used depending on the length of the CI – Bonferroni-selected–Bonferroni-adjusted, Adjusted BH-Selected CIs (Benjamini and Yekutieli 2005). The incentive of choosing one procedure over another is to ensure that the CI is as narrow as possible and to keep the FCR. For microarray experiments and other modern applications, there are a huge number of parameters, often tens of thousands or more and it is very important to choose the most powerful procedure. The FCR was first introduced by Daniel Yekutieli in his PhD thesis in 2001. Not keeping the FCR means when , where is the number of true null hypotheses, is the number of rejected hypothesis, is the number of false positives, and is the significance level. Intervals with simultaneous coverage probability can control the FCR to be bounded by . Classification of multiple hypothesis tests Selection causes reduced average coverage. Selection can be presented as conditioning on an event defined by the data and may affect the coverage probability of a CI for a single parameter. Equivalently, the problem of selection changes the basic sense of P-values. FCR procedures consider that the goal of conditional coverage following any selection rule for any set of (unknown) values for the parameters is impossible to achieve.