Trace regression models are widely used in applications involving panel data, images, genomic microarrays, etc., where high-dimensional covariates are often involved. However, the existing research involving high-dimensional covariates focuses mainly on the condition mean model. In this paper, we extend the trace regression model to the quantile trace regression model when the parameter is a matrix of simultaneously low rank and row (column) sparsity. The convergence rate of the penalized estimator is derived under mild conditions. Simulations, as well as a real data application, are also carried out for illustration.

中文翻译：

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稀疏和低秩分位数迹回归的收敛速度

迹回归模型广泛应用于涉及面板数据、图像、基因组微阵列等的应用中，这些应用中经常涉及高维协变量。然而，现有涉及高维协变量的研究主要集中在条件均值模型上。在本文中，当参数是同时具有低秩和行（列）稀疏性的矩阵时，我们将迹回归模型扩展到分位数迹回归模型。惩罚估计器的收敛速度是在温和条件下得出的。还进行了模拟以及实际数据应用以进行说明。