Quantile Tensor Regression for Integrative Genomic Analysis of Oesophageal Carcinoma

Recent integrative genomic studies have increasingly exploited the tensor structure of multi-omics data to develop statistical methods that jointly model the relationship between clinical outcomes and multiple genomes. However, genomic measurements and clinical outcomes are frequently contaminated by outliers or heavy-tailed noise, necessitating robust tensor-based inference approaches. In this paper, we investigate the quantile tensor regression with an emphasis on the region selection problem. We introduce a novel estimator that integrates quantile regression for robustness with a nonconvex penalty to encourage sparsity in the tensor coefficient, thereby enabling the identification of localized genomic regions that significantly influence the clinical response. To solve the resulting optimization problem, we devise an effective algorithm tailored to the nonconvex objective and tensor architecture. We establish the asymptotic properties of the proposed nonconvex penalized estimator. Extensive simulations demonstrate the excellent finite-sample performance of the proposed estimator. We further illustrate the practical utility of the proposed estimator through an application to esophageal carcinoma data, providing empirical validation.