Functional magnetic resonance imaging (fMRI) is a popular technology that measures brain activity by detecting changes associated with blood flow. Such data could be used to provide information on behavior, brain development trajectories, and metabolic diseases. As the technology advances, we can obtain brain images with higher resolution these days. While traditional methods of analysis may have produced acceptable results when the imaging data was in low resolution, the high dimensional images demand better statistical methods for more precise and efficient estimations for task fMRI studies. We develop novel statistical methodologies for conducting efficient multivariate inferences for fMRI studies.