  Functional magnetic resonance imaging (fMRI) aims to locate activated regions
in human brains when specific tasks are performed. The conventional tool for
analyzing fMRI data applies some variant of the linear model, which is
restrictive in modeling assumptions. To yield more accurate prediction of the
time-course behavior of neuronal responses, the semiparametric inference for
the underlying hemodynamic response function is developed to identify
significantly activated voxels. Under mild regularity conditions, we
demonstrate that a class of the proposed semiparametric test statistics, based
on the local linear estimation technique, follow $\chi^2$ distributions under
null hypotheses for a number of useful hypotheses. Furthermore, the asymptotic
power functions of the constructed tests are derived under the fixed and
contiguous alternatives. Simulation evaluations and real fMRI data application
suggest that the semiparametric inference procedure provides more efficient
detection of activated brain areas than the popular imaging analysis tools AFNI
and FSL.
