Oracle Inequality for Sparse Trace Regression Models with Exponential β-mixing Errors

In applications involving, e.g., panel data, images, genomics microarrays, etc., trace regression models are useful tools. To address the high-dimensional issue of these applications, it is common to assume some sparsity property. For the case of the parameter matrix being simultaneously low rank and elements-wise sparse, we estimate the parameter matrix through the least-squares approach with the composite penalty combining the nuclear norm and the l₁ norm. We extend the existing analysis of the low-rank trace regression with i.i.d. errors to exponential β-mixing errors. The explicit convergence rate and the asymptotic properties of the proposed estimator are established. Simulations, as well as a real data application, are also carried out for illustration.