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(1) Many fMRI analyses assume a canonical hemodynamic response function, but this assumption may lead to inaccurate data models. By adopting the finite impulse response model, we show that voxel\u2010specific hemodynamic response functions can be estimated directly from the data. (2) There is a large amount of low\u2010frequency noise fluctuation (LFF) in blood oxygenation level dependent (BOLD) time\u2010series data. To compensate for this problem, we use polynomials as regressors for LFF. We show that this technique substantially improves SNR and is more accurate than high\u2010pass filtering of the data. (3) Model overfitting is a problem for the finite impulse response model because of the low SNR of the BOLD response. To reduce overfitting, we estimate a hemodynamic response timecourse for each voxel and incorporate the constraint of time\u2010event separability, the constraint that hemodynamic responses across event types are identical up to a scale factor. We show that this technique substantially improves the accuracy of hemodynamic response estimates and can be computed efficiently. For the analysis techniques we present, we evaluate improvement in modeling accuracy via 10\u2010fold cross\u2010validation. 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