Likelihood-based inference for quantile regression using the skewed generalized normal distribution

The asymmetric Laplace (ALP) distribution is commonly used in quantile regression (QR) due to its analytical convenience. However, its moderately heavy tails make it unsuitable for data that strongly deviates from the Gaussian assumption. In this article, we reparameterize a skewed generalized normal (SGN) distribution, with a skewness parameter defined on the interval (0, 1), as a robust alternative to the ALP distribution within a likelihood-based QR framework. We present two stochastic representations of the SGN distribution: one for random sample generation and another that enables efficient maximum likelihood estimation via the Expectation–Maximization (EM) algorithm. By representing the SGN distribution as a scale mixture of skewed normal (SKN) distributions, we derive closed-form updates for the regression parameters. Building on the EM framework, we further develop a case-deletion diagnostics analysis for QR models. The effectiveness and robustness of the proposed method are demonstrated through extensive experiments on both simulated and real-world datasets.