Post-selection inference on high-dimensional varying-coefficient quantile regression model

Abstract

Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. In this work, we study high-dimensional varying-coefficient quantile regression model that allows us to capture non-stationary effects of the input variables across time. We develop new tools for statistical inference that allow us to construct valid confidence intervals and honest tests for nonparametric coefficient at fixed time and quantile. Our focus is on inference in 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. Never the less, we are able to 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. The statistical framework allows us to construct a confidence interval at a fixed point in time and a fixed quantile based on a Normal approximation. We performed numerical simulations to demonstrate the finite sample performance of our method and we also illustrated the application with a real data example.

Publication
arXiv:2002.07370
Ran Dai
Ran Dai
PhD (2016-2020)

Ran Dai is a fourth-year PhD candidate in Statistics at the University of Chicago advised by Rina Foygel Barber. 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.

Mladen Kolar
Mladen Kolar
Associate Professor of Econometrics and Statistics

Mladen Kolar is an Associate Professor of Econometrics and Statistics at 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.

Related