CAREER: A new and pragmatic framework for modeling and predicting conditional quantiles in data-sparse regions

George Washington University, Washington DC

Investigators

Abstract

Quantile regression provides a valuable semiparametric tool for modeling the conditional quantiles of a response variable given predictors. However, making inference for quantile regression is challenging in data-sparse regions such as at low or high quantiles with quantile levels close to 0 or 1. In the proposed research, the Principal Investigator (PI) aims to develop theory and methodology for quantile regression in data-sparse regions, which opens up a significant new direction in quantile regression. For estimating extreme conditional quantiles of the response distribution, the PI plans to develop extrapolation methods based on a novel application of the extreme value theory. In data sparse areas, the formulation of models plays a critical role. The PI will study models with different levels of complexity, which calls for different techniques for quantifying the tail quantiles. New theory and methods for joint quantile estimation and inter-quantile shrinkage will be developed to improve statistical efficiency by sharing information across multiple quantile functions. The PI will also study tail quantile regression for dependent data, where the common understanding about the impact of dependence on statistical inference needs to be re-examined. As a result, new and efficient methods to incorporate tail dependence will be proposed. An important 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. The proposed methodologies will have broad and valuable applications in studies of rare events in climate sciences, risk management in finance, studies of infant birth weights, and prediction of insurance claims. The PI will integrate research and education by developing advanced topics courses, engaging graduate and undergraduate students, especially those from under-represented groups, in the project, and reaching out to the K-12 education levels by training high school teachers.