High‐Dimensional Regression With Missing Data: An Asymptotic Study

ABSTRACT We present an asymptotic analysis of high‐dimensional linear regression with missing data and propose a novel method to approximate leave‐one‐out cross validation, facilitating faster hyperparameter tuning. Our analysis extends beyond standard ridge regression to include adversarial training, introducing a robust formulation specifically designed to handle missing data. Building upon existing literature in reguralization, who addressed complete data settings, our framework establishes asymptotic properties of regression models with missing data. Notably, we are the first to explore cross‐validation for adversarial training in finite‐sample regimes where the loss functions is nondifferentiable. Our cross‐validation approximation demonstrates substantial computational advantages over traditional methods.