Multivariate factorizable expectile regression with application to fMRI data

A multivariate expectile regression model is proposed to analyze the tail events of large cross-sectional and spatial data, when the tail events are linked by a latent factor structure. The computational advantage of the method is demonstrated, and the estimation risk is analyzed for every fixed number of iteration and fixed sample size, when the latent factors are either exactly or approximately sparse. The proposed method is applied on the functional magnetic resonance imaging (fMRI) data taken during an experiment of investment decisions making. It is shown that the negative extreme blood oxygenation level dependent (BOLD) responses may be relevant to the risk preferences.