Inference for high-dimensional varying-coefficient quantile regression
Abstract
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or time. In this work, we study high-dimensional varying-coefficient quantile regression models and develop new tools for statistical inference. We focus on development of valid confidence intervals and honest tests for nonparametric coefficients at a fixed time point and quantile, while allowing for a high-dimensional setting where the number of input variables exceeds the sample size. Performing statistical inference in this regime is challenging due to the usage of model selection techniques in estimation. Nevertheless, we can develop valid inferential tools that are applicable to a wide range of data generating processes and do not suffer from biases introduced by model selection. We performed numerical simulations to demonstrate the finite sample performance of our method, and we also illustrated the application with a real data example.
Type
Publication
Electronic Journal of Statistics, 15(2)
Authors
PhD (2016-2020)
Ran Dai received her PhD in Statistics at the University of Chicago in July 2020. Ran’s research interest is in high dimensional inference, nonparametric modeling, and shape-constrained regressions, multiple testing, and causal inference. In particular, Ran is interested in developing computationally efficient algorithms for these problems with statistical convergence guarantee and valid inference; and applying these methods towards real datasets in the areas of drug development, HIV mutation study and cancer study.
Authors
Professor of Data Sciences and Operations
Mladen Kolar is a Professor of Data Sciences and Operations at the University of Southern California Marshall School of Business and a Visiting Professor of Statistics and Data Science at Mohamed bin Zayed University of Artificial Intelligence. Before joining USC, he was on the faculty of the University of Chicago Booth School of Business. His research is focused on high-dimensional statistical methods, graphical models, varying-coefficient models and data mining, driven by the need to uncover interesting and scientifically meaningful structures from observational data. He is a Fellow of the Institute of Mathematical Statistics.