Cross-Validation, Risk Estimation, and Model Selection

Stefan Wager

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arXiv · 1909.11696

Cross-Validation, Risk Estimation, and Model Selection

Stefan Wager

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Abstract

Cross-validation is a popular non-parametric method for evaluating the accuracy of a predictive rule. The usefulness of cross-validation depends on the task we want to employ it for. In this note, I discuss a simple non-parametric setting, and find that cross-validation is asymptotically uninformative about the expected test error of any given predictive rule, but allows for asymptotically consistent model selection. The reason for this phenomenon is that the leading-order error term of cross-validation doesn't depend on the model being evaluated, and so cancels out when we compare two models.

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Stefan Wager. 2019-09-25. Cross-Validation, Risk Estimation, and Model Selection. https://arxiv.org/abs/1909.11696

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