Tensor Ring Quantile Regression

Key Points

• This research aims to address the challenges of traditional quantile regression in handling tensor data with complex relationships.
• Introduced a tensor ring decomposition technique.
• Developed a new tensor ring quantile regression model.
• Proved consistency, asymptotic normality, and efficacy in low-dimensional settings.
• Introduced l1 penalty estimator and established error bounds in high-dimensional scenarios.
• Simulation and empirical studies demonstrate superior estimation and prediction performance.
• The model effectively captures relationships among tensor-valued covariates and scalar responses.