Confidence Intervals and Hypothesis Testing for High-dimensional Quantile Regression: Convolution Smoothing and Debiasing

$\ell_1$-penalized quantile regression ($\ell_1$-QR) is a useful tool for modeling the relationship between input and output variables when detecting heterogeneous effects in the high-dimensional setting. Hypothesis tests can then be formulated based on the debiased $\ell_1$-QR estimator that reduces the bias induced by Lasso penalty. However, the non-smoothness of the quantile loss brings great challenges to the computation, especially when the data dimension is high. Recently, the convolution-type smoothed quantile regression (SQR) model has been proposed to overcome such shortcoming, …

bias confidence convolution effects hypothesis lasso modeling quantile regression relationship testing tests tool variables