Overparametrized linear regression with noisy and missing data

초록

In this paper, we investigate the performance of overparametrized linear regression models in scenarios involving noisy observations, missing data at random, and response outliers. We propose a novel Corrected Minimum Norm Interpolation (C-MNI) estimator to handle errors-in-variables (EIV) and missing datasets. Additionally, we develop a Robust Minimum Norm Interpolation (Robust MNI) estimator to effectively address response contamination by outliers. Our work successfully extends the arguments of Bartlett et al. (2020) to accommodate cases where observed data are imperfect, resulting in discrepancies between observed and true values. The main contribution of this study is the derivation of theoretical risk bounds for our proposed estimators, which notably generalize and extend the bound established by Bartlett et al. (2020). Our theoretical analysis is empirically validated through extensive simulation analyses across various realistic settings, which confirm the superior predictive accuracy and robustness of our proposed methods compared to conventional estimators.

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