Assessing mean and median filters in multiple testing for large-scale imaging data

A new multiple testing procedure, called the FDR<Subscript> L </Subscript> procedure, was proposed by Zhang et al. (Ann Stat 39:613–642, <CitationRef CitationID="CR12">2011</CitationRef>) for detecting the presence of spatial signals for large-scale 2D and 3D imaging data. In contrast to the conventional multiple testing procedure, the FDR<Subscript> L </Subscript> procedure substitutes each p-value by a locally aggregated median filter of p-values. This paper examines the performance of another commonly used filter, mean filter, in the FDR<Subscript> L </Subscript> procedure. It is demonstrated that when the p-values are independent and uniformly distributed under the true null hypotheses, (i) in view of estimating the resulting false discovery rate, the mean filter better alleviates the “lack of identification phenomenon” of the FDR<Subscript> L </Subscript> procedure than the median filter; (ii) in view of signal detection, the median filter enjoys the “edge-preserving property” and lends support to its better performance in detecting sparse signals than the mean filter. Copyright Sociedad de Estadística e Investigación Operativa 2014