In recent years, there has been a significant growth in research focusing on
minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators.
However, the majority of these analyses have been limited to a simple
regression error structure, assuming independent and identically distributed
errors with zero mean and common variance, independent of the feature vectors.
Additionally, the main focus of these theoretical analyses has been on the
out-of-sample prediction risk. This paper breaks away from the existing
literature by examining the mean squared error of the ridgeless interpolation
least squares estimator, allowing for more general assumptions about the
regression errors. Specifically, we investigate the potential benefits of
overparameterization by characterizing the mean squared error in a finite
sample. Our findings reveal that including a large number of unimportant
parameters relative to the sample size can effectively reduce the mean squared
error of the estimator. Notably, we establish that the estimation difficulties
associated with the variance term can be summarized through the trace of the
variance-covariance matrix of the regression errors.

本文从均方误差的角度对 ridgeless interpolation least squares estimator 进行分析，证明相对于样本大小引入大量不重要的参数能够有效降低估计器的均方误差，并且利用回归误差的方差 - 协方差矩阵的迹来刻画估计困难。