The spatial signals in neuroimaging mass univariate analyses can be characterized in a number of ways, but one widely used approach is peak inference: the identification of peaks in the image. Peak locations and magnitudes provide a useful summary of activation and are routinely reported, however, the magnitudes reflect selection bias as these points have both survived a threshold and are local maxima. In this paper we propose the use of resampling methods to estimate and correct this bias in order to estimate both the raw units change as well as standardized effect size measured with Cohen's d and partial R 2 . We evaluate our method with a massive open dataset, and discuss how the corrected estimates can be used to perform power analyses. 1 In voxelwise inference voxels with test statistic values lying above a multiple testing threshold are determined to be significant. In both peak and cluster level inference a primary threshold is used to identify peaks/clusters and then thresholding based on peak magnitude and cluster extent is used to determine significant peaks/clusters.
Given a functional central limit (fCLT) and a parameter transformation, we use the functional delta method to construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the transformed limit process. Moreover, we prove a multiplier bootstrap fCLT theorem for these transformed residuals and show how this can be used to construct simultaneous confidence bands for transformed functional parameters. As motivation for this methodology, we provide the formal application of these residuals to a functional version of the effect size parameter Cohen's d, a problem appearing in current brain imaging applications. The performance and necessity of such residuals is illustrated in a simulation experiment for the covering rate of simultaneous confidence bands for the functional Cohen's d parameter.
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