Testing the prediction error difference between 2 predictors

We develop an inference framework for the difference in errors between 2 prediction procedures. The 2 procedures may differ in any aspect and possibly utilize different sets of covariates. We apply training and testing on the same data set, which is accommodated by sample splitting. For each split, both procedures predict the response of the same samples, which results in paired residuals to which a signed-rank test is applied. Multiple splits result in multiple p-values. The median p-value and the mean inverse normal transformed p-value are proposed as summary (test) statistics, for which bounds on the overall type I error rate under a variety of assumptions are proven. A simulation study is performed to check type I error control of the least conservative bound. Moreover, it confirms superior power of our method with respect to a one-split approach. Our inference framework is applied to genomic survival data sets to study 2 issues: compare lasso and ridge regression and decide upon use of both methylation and gene expression markers or the latter only. The framework easily accommodates any prediction paradigm and allows comparing any 2, possibly nonmodel-based, prediction procedures.