This paper establishes oracle inequalities for the prediction risk of the empirical risk minimizer for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the cases of identically and heterogeneously distributed observations. Our analysis is nonparametric in the sense that the relationship between the regressand and the regressors is assumed to be unknown. The main results of this paper indicate that the empirical risk minimizer achieves the optimal performance (up to a logarithmic factor) in a dependent data setting.
翻译:本文为大维线性回归实验风险最小化的预测风险设定了甲骨文不平等。 我们通过允许数据依赖性和重尾化来概括现有结果。 分析涵盖了相同和不同分布的观测案例。 我们的分析是非对称的,因为假设回归和回归器之间的关系不明。 本文的主要结果表明,实验风险最小化者在依赖性数据设置中实现了最佳性能( 直至对数系数 )。