In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of p-values under the null hypothesis and the other component f is nonparametric and stands for the distribution under the alternative hypothesis. Motivated by the issue of local false discovery rate estimation, we focus here on the estimation of the nonparametric unknown component f in the mixture, relying on a preliminary estimator of the unknown proportion θ of true null hypotheses. We propose and study the asymptotic properties of two different estimators for this unknown component. The first estimator is a randomly weighted kernel estimator. We establish an upper bound for its pointwise quadratic risk, exhibiting the classical nonparametric rate of convergence over a class of Hölder densities. To our knowledge, this is the first result establishing convergence as well as corresponding rate for the estimation of the unknown component in this nonparametric mixture. The second estimator is a maximum smoothed likelihood estimator. It is computed through an iterative algorithm, for which we establish a descent property. In addition, these estimators are used in a multiple testing procedure in order to estimate the local false discovery rate. Their respective performances are then compared on synthetic data.

This paper tests for output convergence across n = 51 economies, employing the definition of Pesaran [Journal of Econometrics 138, 312–355 (2007)]. The definition requires output gaps to be stationary around a constant mean. But when all n(n − 1)/2 pairs of log per capita output gaps are considered, this results in more than 1,000 unit root tests to be conducted. Hence, because of the ensuing multiplicity of the testing problem, a nontrivial number of output gaps will be falsely declared to be stationary when each of the n(n − 1)/2 hypotheses is tested at some conventional level like 5%. To solve the problem, we employ recent multiple testing techniques that allow us to bound the expected fraction of false rejections at a desired level. Monte Carlo results illustrate the usefulness of the techniques. The empirical results show that the data do not support the notion of output convergence after controlling for multiplicity.

Recently, Macgregor et al. (2009) demonstrated significant associations of ADH polymorphisms with reactions to alcohol and alcohol consumption measures in an Australian sample. The aim of the present study was to replicate these findings in a Dutch sample. Survey data on alcohol phenotypes came from 1,754 unrelated individuals registered with the Netherlands Twin Register. SNPs in the ADH gene cluster located on chromosome 4q (n = 491) were subdivided in seven gene sets: ADH5, ADH4, ADH6, ADH1A, ADH1B, ADH1C and ADH7. Within these sets associations of SNPs with alcohol consumption measures, age at onset variables, reactions to alcohol and problem drinking liability were examined. Of the original 38 SNPs studied by Macgregor et al. (2009), six SNPs were not available in our dataset, because one of them had a minor allele frequency < .01 (rs1229984) and five could not be imputed. The remaining SNP associations with alcohol phenotypes as identified by Macgregor et al. (2009) were not replicated in the Dutch sample, after correcting for multiple genotype and phenotype testing. Significant associations were found however, for reactions to alcohol with a SNP in ADH5 (rs6827292, p = .001) and a SNP just upstream of ADH5 (rs6819724, p = .0007) that is in strong LD with rs6827292. Furthermore, an association between age at onset of regular alcohol use and a SNP just upstream of ADH7 (rs2654849, p = .003) was observed. No significant associations were found for alcohol consumption and problem drinking liability. Although these findings do not replicate the earlier findings at the SNP level, the results confirm the role of the ADH gene cluster in alcohol phenotypes.

In the problem of large-scale multiple testing the p-plot is a graphically based competitor to the notoriously weak Bonferroni method. The p-plot is less stringent and more revealing in that it gives a gauge of how many hypotheses are decidedly false. The method is elucidated and extended here: the bootstrap reveals bias and sampling error in the usual point estimates, a bootstrap-based confidence interval for the gauge is given, as well as two acceptably powerful blanket tests of significance. Guidelines for use are given, and interpretational pitfalls pointed out, in the discussion of a case study linking premortem neuropsychological and postmortem neuropathologic data in an HIV cohort study. (JINS, 1999, 5, 510–517)