Provable More Data Hurt in High Dimensional Least Squares Estimator

Zeng Li, Chuanlong Xie, QINWEN WANG

Abstract: This paper investigates the finite-sample prediction risk of the high-dimensional least squares estimator. We derive the central limit theorem for the prediction risk when both the sample size and the number of features tend to infinity. Furthermore, the finite-sample distribution and the confidence interval of the prediction risk are provided. Our theoretical results demonstrate the sample-wise non-monotonicity of the prediction risk and confirm ''more data hurt'' phenomenon.

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