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Functional magnetic resonance imaging (fMRI) aims to locate activated regionsin human brains when specific tasks are performed. The conventional tool foranalyzing fMRI data applies some variant of the linear model, which isrestrictive in modeling assumptions. To yield more accurate prediction of thetime-course behavior of neuronal responses, the semiparametric inference forthe underlying hemodynamic response function is developed to identifysignificantly activated voxels. Under mild regularity conditions, wedemonstrate that a class of the proposed semiparametric test statistics, basedon the local linear estimation technique, follow $\chi^2$ distributions undernull hypotheses for a number of useful hypotheses. Furthermore, the asymptoticpower functions of the constructed tests are derived under the fixed andcontiguous alternatives. Simulation evaluations and real fMRI data applicationsuggest that the semiparametric inference procedure provides more efficientdetection of activated brain areas than the popular imaging analysis tools AFNIand FSL.

Semiparametric detection of significant activation for brain fMRI