Classes of Multiple Decision Functions Strongly Controlling FWER and FDR

This paper provides two general classes of multiple decision functions where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR). These classes offer the possibility that an optimal multiple decision function with respect to a pre-specified criterion, such as the missed discovery rate (MDR), could be found within these classes. Such multiple decision functions can be utilized in multiple testing, specifically, but not limited to, the analysis of high-dimensional microarray data sets.Comment: 19 page

Adaptive false discovery rate control under independence and dependence

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On empirical distribution function of high-dimensional Gaussian vector components with an application to multiple testing

International audienceThis paper introduces a new framework to study the asymptotical behavior of the empirical distribution function (e.d.f.) of Gaussian vector components, whose correlation matrix Γ(m) is dimension-dependent. Hence, by contrast with the existing literature, the vector is not assumed to be stationary. Rather, we make a "vanishing second order" assumption ensuring that the covariance matrix Γ(m) is not too far from the identity matrix, while the behavior of the e.d.f. is affected by Γ(m) only through the sequence γm=m−2∑i≠jΓ(m)i,j, as m grows to infinity. This result recovers some of the previous results for stationary long-range dependencies while it also applies to various, high-dimensional, non-stationary frameworks, for which the most correlated variables are not necessarily next to each other. Finally, we present an application of this work to the multiple testing problem, which was the initial statistical motivation for developing such a methodology

Adaptive false discovery rate control under independence and dependence

In the context of multiple hypothesis testing, the proportion p 0 of true null hypotheses in the pool of hypotheses to test often plays a crucial role, although it is generally unknown a priori. A testing procedure using an implicit or explicit estimate of this quantity in order to improve its efficency is called adaptive. In this paper, we focus on the issue of false discovery rate (FDR) control and we present new adaptive multiple testing procedures with control of the FDR. In a first part, assuming independence of the p-values, we present two new procedures and give a unified review of other existing adaptive procedures that have provably controlled FDR. We report extensive simulation results comparing these procedures and testing their robustness when the independence assumption is violated. The new proposed procedures appear competitive with existing ones. The overall best, though, is reported to be Storey's estimator, albeit for a specific parameter setting that does not appear to have been considered before. In a second part, we propose adaptive versions of step-up procedures that have provably controlled FDR under positive dependence and unspecified dependence of the p-values, respectively. In the latter case, while simulations only show an improvement over non-adaptive procedures in limited situations, these are to our knowledge among the first theoretically founded adaptive multiple testing procedures that control the FDR when the p-values are not independent

On the false discovery proportion convergence under Gaussian equi-correlation

We study the convergence of the false discovery proportion (FDP) of the Benjamini-Hochberg procedure in the Gaussian equi-correlated model, when the correlation [rho]m converges to zero as the hypothesis number m grows to infinity. In this model, the FDP converges to the false discovery rate (FDR) at rate {min(m,1/[rho]m)}1/2, which is different from the standard convergence rate m1/2 holding under independence.False discovery rate Donsker theorem Equi-correlation Functional Delta method p-value

On least favorable configurations for step-up-down tests

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Tiempo e historia en el teatro del Siglo de Oro

Aprovechar las enseñanzas de la Historia, recurrir al pasado remoto o reciente para mostrar en sus héroes, recreados por el teatro, su dimensión arquetípica y modélica, tales son los propósitos de la dramatización de la materia histórica durante el Siglo de Oro español. La Historia no sólo sirvió de mero marco temporal para ubicar la acción dramática de las piezas en un contexto preciso. Las variaciones, anacronismos evidentes o sincronismos implícitos, a partir dde las fuentes manejadas deben leerse como verdaderas estrategias del dramaturgo. El anclaje histórico de los argumentos, mediante juegos de simetrías y contrastes entre realidad y ficción, enfoca la recepción ideológica de las obras. La poética del tiempo histórico en el teatro se pone al servicio de la emergencia de una conciencia nacional: representar el pasado supone mejor decir y cuestionar el presente. Este libro examina también la estética de la temporalidad que nace de las variaciones cronológicas en las obras contempladas. Las diferentes contribuciones de los autores revelan la distancia tomada por los dramaturgos del Siglo de Oro respecto a la preceptiva clásica. Semejante actitud no exenta de críticas en su época, demuestra la libertad con la que aquellos creadores supieron superar los apremios teóricos de la unidad de tiempo a favor de un dinamismo celebrado en su tiempo por el público heterogéneo y exigente de los corrales