Inference for high-dimensional varying-coefficient quantile regression

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.