We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away from the real axis. We extend this work by proving quantitative bounds involving both the dimensions and the spectral parameter, in particular allowing it to get closer to the real positive semi-line. As applications, we obtain a new bound for the convergence in Kolmogorov distance of the empirical spectral distributions of these general models. We also apply our framework to the problem of regularization of Random Features models in Machine Learning without Gaussian hypothesis.

翻译：我们用一.d.列研究从矩形随机矩阵中产生的共变矩阵样本,以前曾知道这些矩阵的固态在光谱参数与实际轴保持距离时具有确定等值。我们通过证明涉及尺寸和光谱参数的定量界限来扩展这项工作,特别是使它更接近真正的正半线。作为应用,我们获得了在科尔莫戈罗夫距离内将这些一般模型的经验光谱分布相趋一致的新线。我们还运用了我们的框架来解决机械学习中随机特征模型的正规化问题,而没有高斯假设。