8:30AM - Halsey Hall Room 120
Analysis of Extreme Conditional Quantiles
An essential problem in many fields is the modeling and prediction of events that are rare but have significant consequences. Unexpectedly heavy rainfall, large portfolio loss, and dangerously low birth weight are some examples of rare events. For such events, scientists are particularly interested in modeling and estimating the tail quantiles of the underlying distribution rather than the central summaries, such as the mean or median. Quantile regression provides a valuable semiparametric tool for modeling the conditional quantiles of a response variable given predictors. However, it is challenging to make inference in data-sparse regions such as at extremely low or high quantiles with quantile levels close to zero or one. In this talk, I will present some recently developed estimation methods for extreme conditional quantiles based on the application of the extreme value theory and quantile regression. In data-sparse areas, the formulation of models plays a critical role. I will discuss the problem under various models with different levels of complexity, which calls for different techniques for quantifying the tail behaviors. Asymptotic theory and empirical studies will be presented to demonstrate the properties and value of the proposed methods.