New blockwise permutation tests preserving exchangeability in functional neuroimaging

In this paper, we present a new blockwise permutation test approach based on the moments of the test statistic. The method is of importance to functional neuroimaging studies. In order to preserve the exchangeability condition required in permutation, we divide the time series into certain exchangeability blocks. In addition, efficient moments-based permutation tests are performed by approximating the permutation distribution of the test statistic with the Pearson distribution series. This involves the calculation of the first four moments of the permutation distribution within each block and then over the whole time series. The accuracy and efficiency of the proposed method are demonstrated using both simulated time series and fMRI data.