Using larger dimensional signal subspaces to increase sensitivity in fMRI time series analyses

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Abstract
It has been explained previously how using large dimensional signal‐subspaces can reduce/eliminate bias in the estimated fMRI response (Burock and Dale [2000]: Hum Brain Mapp 11:249–260). It has also been explained how one can project this less biased estimate onto a one‐dimensional subspace of interest (Burock and Dale [2000]: Hum Brain Mapp 11:249–260). In cases where there are multiple, correlated characterized response components per event type, separately projecting the full hemodynamic response onto one‐dimensional subspaces of interest can lead to bias. We present an approach for both estimating the full hemodynamic response and obtaining from it unbiased estimates of effects of theoretical interest (in the context of ordinary least‐squares estimation). The latter estimates are identical to those obtained by projecting the original data into the space defined by the (possibly multi‐dimensional) effects of theoretical interest, but the ensuing statistical inference can be more sensitive. Hum. Brain Mapping 17:13–16, 2002.