This article considers ultrahigh-dimensional forecasting problems with survival response variables. We propose a two-step model averaging procedure for improving the forecasting accuracy of the true conditional mean of a survival response variable. The first step is to construct a class of candidate models, each with low-dimensional covariates. For this, a feature screening procedure is developed to separate the active and inactive predictors through a marginal Buckley–James index, and to group covariates with a similar index size together to form regression models with survival response variables. The proposed screening method can select active predictors under covariate-dependent censoring, and enjoys sure screening consistency under mild regularity conditions. The second step is to find the optimal model weights for averaging by adapting a delete-one cross-validation criterion, without the standard constraint that the weights sum to one. The theoretical results show that the delete-one cross-validation criterion achieves the lowest possible forecasting loss asymptotically. Numerical studies demonstrate the superior performance of the proposed variable screening and model averaging procedures over existing methods.

本文考虑了具有生存响应变量的超高维预测问题。我们提出了两步模型平均程序，以提高生存反应变量的真实条件均值的预测准确性。第一步是构造一类候选模型，每个候选模型都具有低维协变量。为此，开发了一种特征筛选程序，以通过边际Buckley-James索引来区分活跃和不活跃的预测变量，并将具有相似索引大小的协变量分组在一起，以形成具有生存响应变量的回归模型。所提出的筛选方法可以在依赖协变量的审查条件下选择活跃的预测指标，并在温和规律的条件下享有确定的筛选一致性。第二步是通过适应删除一交叉验证准则来找到用于平均的最佳模型权重，而没有权重之和为一的标准约束。理论结果表明，删除一交叉验证准则渐近地实现了最低的预测损失。数值研究表明，提出的变量筛选和模型平均程序优于现有方法的优越性能。