标题： 交叉验证在比较回归方法中的一致性 显示英文标题

标题： Consistency of cross validation for comparing regression procedures

摘要： 交叉验证（CV）的理论发展主要集中在从一组有限维模型（例如，线性回归中的子集或阶数选择）中选择一个，或者选择一个平滑参数（例如，核平滑的带宽）。 然而，当应用于比较参数方法和非参数方法之间或在非参数方法内部时，关于交叉验证的一致性知之甚少。 我们证明，在某些条件下，通过适当选择数据分割比例，交叉验证在选择更好程序方面是一致的，即概率趋近于1。 我们的结果揭示了交叉验证有趣的行为。 当比较两个以相同非参数速率收敛的模型（程序）时，与参数情况相反，交叉验证中用于评估的数据比例不需要在规模上占主导地位。 此外，它甚至可以比用于估计的比例更小，而不会影响一致性属性。 显示英文摘要

摘要： Theoretical developments on cross validation (CV) have mainly focused on selecting one among a list of finite-dimensional models (e.g., subset or order selection in linear regression) or selecting a smoothing parameter (e.g., bandwidth for kernel smoothing). However, little is known about consistency of cross validation when applied to compare between parametric and nonparametric methods or within nonparametric methods. We show that under some conditions, with an appropriate choice of data splitting ratio, cross validation is consistent in the sense of selecting the better procedure with probability approaching 1. Our results reveal interesting behavior of cross validation. When comparing two models (procedures) converging at the same nonparametric rate, in contrast to the parametric case, it turns out that the proportion of data used for evaluation in CV does not need to be dominating in size. Furthermore, it can even be of a smaller order than the proportion for estimation while not affecting the consistency property.