A generalized sigmoidal quantile function approach to smoothed quantile regression

Recent advancements in smoothing techniques for quantile regression have addressed critical challenges in statistical inference, such as non-smooth objective functions and slow convergence rates. Building on this progress, we extend our work on the Generalized Sigmoidal Quantile Function–a novel smoothed quantile estimator based on an alternative formulation of the population quantile–to the regression setting, introducing the Generalized Sigmoidal Conditional Quantile Function. This new framework employs a smooth approximation of the absolute value function, enhancing both asymptotic properties and computational efficiency. We demonstrate that the Generalized Sigmoidal Conditional Quantile Function estimator belongs to the broad class of M-estimators. Additionally, we establish theoretical properties, conduct extensive simulation studies, and validate its practical utility through a real-world modeling example.