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