  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.
