Nonparametric inference of the hemodynamic response using multi-subject fMRI data

Estimation and inferences for the hemodynamic response functions (HRF) using multi-subject fMRI data are considered. Within the context of the General Linear Model, two new nonparametric estimators for the HRF are proposed. The first is a kernel-smoothed estimator, which is used to construct hypothesis tests on the entire HRF curve, in contrast to only summaries of the curve as in most existing tests. To cope with the inherent large data variance, we introduce a second approach which imposes Tikhonov regularization on the kernel-smoothed estimator. An additional bias-correction step, which uses multi-subject averaged information, is introduced to further improve efficiency and reduce the bias in estimation for individual HRFs. By utilizing the common properties of brain activity shared across subjects, this is the main improvement over the standard methods where each subject's data is usually analyzed independently. A fast algorithm is also developed to select the optimal regularization and smoothing parameters. The proposed methods are compared with several existing regularization methods through simulations. The methods are illustrated by an application to the fMRI data collected under a psychology design employing the Monetary Incentive Delay (MID) task.