The statistical inference based on the ordinary least squares regression is sub-optimal when the distributions are skewed or when the quantity of interest is the upper or lower tail of the distributions. For example, the changes in Total Sharp Scores (TSS), the primary measurements of the...

Data do not always obey the normality assumption, and outliers can have dramatic impacts on the quality of the least squares methods. We use Huber's loss function in developing robust methods for time-course multivariate responses. We use spline basis expansion of the time-varying regression...

We proposed a method to estimate extreme conditional quantiles by combining quantile GARCH model of Xiao and Koenker (2009) and extreme value theory (EVT) approach. We first estimate the latent volatility process using the information of intermediate quantiles. We then apply EVT to the tail...