bce9abf229ffd7e570818476ee5d7dde-Supplemental.pdf

We first prove a general asymptotic linearity result for repeated sample-splitting estimators. Thm. 1 follows from the next more general result, which establishes the asymptotic normality of k -fold CV with independent (not necessarily identically distributed) data. Under the notation of Prop. 1, suppose that the datapoints (Z Additionally, if (2.2) holds in probability, then Under Lindeberg's condition, we get the first convergence result thanks to Lindeberg's Central Limit Theorem (see [10, Thm. Additionally, if assumption (2.2) holds, we apply Prop. 1 and Slutsky's theorem to get the second convergence result.If the ( Z Thm. 2 will follow from the following more general result. We now state a conditional application of a version of the Efron-Stein inequality due to Steele [47]. We then note that the asymptotic linearity condition (2.2) in L Therefore, Thm. 2 follows from Thm. 7. Thm. 3 will follow from the following more general statement.