False discovery and false nondiscovery rates in single-step multiple testing procedures

Results on the false discovery rate (FDR) and the false nondiscovery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these results extend previously known results, providing further insights, particularly under dependence, into the notions of FDR and FNR and related measures. First, considering fixed configurations of true and false null hypotheses, inequalities are obtained to explain how an FDR- or FNR-controlling single-step procedure, such as a Bonferroni or \u{S}id\'{a}k procedure, can potentially be improved. Two families of procedures are then constructed, one that modifies the FDR-controlling and the other that modifies the FNR-controlling \u{S}id\'{a}k procedure. These are proved to control FDR or FNR under independence less conservatively than the corresponding families that modify the FDR- or FNR-controlling Bonferroni procedure. Results of numerical investigations of the performance of the modified \u{S}id\'{a}k FDR procedure over its competitors are presented. Second, considering a mixture model where different configurations of true and false null hypotheses are assumed to have certain probabilities, results are also derived that extend some of Storey's work to the dependence case.Comment: Published at http://dx.doi.org/10.1214/009053605000000778 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Selection Bias Correction and Effect Size Estimation under Dependence

We consider large-scale studies in which it is of interest to test a very large number of hypotheses, and then to estimate the effect sizes corresponding to the rejected hypotheses. For instance, this setting arises in the analysis of gene expression or DNA sequencing data. However, naive estimates of the effect sizes suffer from selection bias, i.e., some of the largest naive estimates are large due to chance alone. Many authors have proposed methods to reduce the effects of selection bias under the assumption that the naive estimates of the effect sizes are independent. Unfortunately, when the effect size estimates are dependent, these existing techniques can have very poor performance, and in practice there will often be dependence. We propose an estimator that adjusts for selection bias under a recently-proposed frequentist framework, without the independence assumption. We study some properties of the proposed estimator, and illustrate that it outperforms past proposals in a simulation study and on two gene expression data sets.Comment: 21 pages, 2 figure

Gap bootstrap methods for massive data sets with an application to transportation engineering

In this paper we describe two bootstrap methods for massive data sets. Naive applications of common resampling methodology are often impractical for massive data sets due to computational burden and due to complex patterns of inhomogeneity. In contrast, the proposed methods exploit certain structural properties of a large class of massive data sets to break up the original problem into a set of simpler subproblems, solve each subproblem separately where the data exhibit approximate uniformity and where computational complexity can be reduced to a manageable level, and then combine the results through certain analytical considerations. The validity of the proposed methods is proved and their finite sample properties are studied through a moderately large simulation study. The methodology is illustrated with a real data example from Transportation Engineering, which motivated the development of the proposed methods.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS587 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Structural Change in Covariance and Exchange Rate Pass-Through: The Case of Canada

The authors address empirically the implications of structural breaks in the variance-covariance matrix of inflation and import prices for changes in pass-through. They define pass-through within a correlated vector autoregression (VAR) framework as the response of domestic inflation to an impulse in import price inflation. This approach allows them to examine changes in both the amount and the duration of pass-through.Econometric and statistical methods