Robust Integrative Analysis via Quantile Regression with Homogeneity and Sparsity

Integrative analysis plays a critical role in integrating heterogeneous data from multiple datasets to provide a comprehensive view of the overall data features. However, in multiple datasets, outliers and heavy-tailed data can render least squares estimation unreliable. In response, we propose a Robust Integrative Analysis via Quantile Regression (RIAQ) that accounts for homogeneity and sparsity in multiple datasets. The RIAQ approach is not only able to identify latent homogeneous coefficient structures but also recover the sparsity of high-dimensional covariates via double penalty terms. The integration of sample information across multiple datasets improves estimation efficiency, while a sparse model improves model interpretability. Furthermore, quantile regression allows the detection of subgroup structures under different quantile levels, providing a comprehensive picture of the relationship between response and high-dimensional covariates. We develop an efficient alternating direction method of multipliers (ADMM) algorithm to solve the optimization problem and study its convergence. We also derive the parameter selection consistency of the modified Bayesian information criterion. Numerical studies demonstrate that our proposed estimator has satisfactory finite-sample performance, especially in heavy-tailed cases.