Cross-Validation for Correlated Data

K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional assumptions cannot be taken. However, CV with squared error loss is not free from distributional assumptions, in particular in cases involving non-iid data. This article analyzes CV for correlated data. We present a criterion for suitability of standard CV in presence of correlations. When this criterion does not hold, we introduce a bias corrected CV estimator which we termthat yields an unbiased estimate of prediction error in many settings where standard CV is invalid. We also demonstrate our results numerically, and find that introducing our correction substantially improves both, model evaluation and model selection in simulations and real data studies.for this article are available online.

Automated summary

This article analyzes the application of K-fold cross-validation in correlated data and introduces a criterion and a correction method, which significantly improves the performance of model evaluation and selection.