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In recent years, there has been a significant growth in research focusing onminimum $\ell_2$ norm (ridgeless) interpolation least squares estimators.However, the majority of these analyses have been limited to a simpleregression error structure, assuming independent and identically distributederrors with zero mean and common variance. In this paper, we explore predictionrisk as well as estimation risk under more general regression errorassumptions, highlighting the benefits of overparameterization in a finitesample. We find that including a large number of unimportant parametersrelative to the sample size can effectively reduce both risks. Notably, weestablish that the estimation difficulties associated with the variancecomponents of both risks can be summarized through the trace of thevariance-covariance matrix of the regression errors.

Prediction Risk and Estimation Risk of the Ridgeless Least Squares Estimator under General Assumptions on Regression Errors