Nonparametric Quantile Regression

Nonparametric quantile regression aims to model the conditional quantiles of a response variable given predictor variables without assuming a specific functional form, offering a more flexible approach than traditional parametric methods. Recent research heavily focuses on using deep neural networks, particularly those employing rectified linear unit (ReLU) or ReQU activation functions, coupled with novel penalty functions to ensure the crucial non-crossing property of quantile curves across different quantile levels. This allows for robust estimation of the entire quantile regression process, leading to improved accuracy and the construction of reliable conformal prediction intervals. These advancements enhance the applicability of quantile regression in diverse fields requiring robust and flexible modeling of conditional distributions.