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.