Functional Magnetic Resonance Imaging (fMRI) is a medical-imaging technique for studying brain function. It can be used to capture the response of the brain to various tasks. The response to a brief, intense period of neural stimulation is called the hemodynamic response function (HRF). Modeling HRF is essential to identifying the brain activation by exploring the relationship between the experimental stimulus and the response. In this dissertation, we discuss three research problems related to HRF estimation. First, when multiple types of stimuli are present, how can we capture the characteristic HRF for each stimulus? Second, is there any difference among the HRFs corresponding to multiple stimuli? Third, how can we improve the HRF estimator's efficiency? We propose a nonparametric method, transfer function estimate (TFE), to answer these three questions. Building on existing work, we extend the nonparametric approach to a multivariate form, which adapts to the multiple types of stimuli, and we develop hypothesis testing to identify the brain activation and to compare the HRFs under different stimuli. In order to improve estimation efficiency, we propose using weighted least square (WLS) in a multiple system of regression by spectral methods. The finite-sample performance of the TFE is illustrated through several simulation studies and real fRMI data sets. We also establish the asymptotic normality of the TFE, as well as the efficiency of the WLS estimator.