Randomized trial reveals robust performance of tensor quantile regression, indicating improved accuracy over traditional methods.
Key Points
This research aims to develop a robust tensor quantile regression method to handle tensor-valued covariates while addressing the fragility of traditional regression approaches.
Implemented CP decomposition for dimension reduction of tensor-valued data.
Employed an exponential-type penalty for element-wise sparse variable selection.
Utilized an efficient algorithm based on the ADMM framework for computation.
Demonstrated improved signal recovery and estimation accuracy compared to conventional vectorized quantile regression.
Achieved superior predictive performance in simulations with varying sparse signal settings.
Analysis of the Beijing dataset showed pronounced effects of major air pollutants with spatial and quantile heterogeneity.