Optimal model averaging forecasting in high-dimensional survival analysis

TL;DR

This paper introduces a two-step model averaging approach for high-dimensional survival analysis, combining feature screening with optimal weight selection to enhance forecasting accuracy.

Contribution

It develops a novel feature screening method for survival data and an unconstrained model averaging technique with proven asymptotic optimality.

Findings

Outperforms existing methods in numerical simulations

Ensures sure screening consistency under mild conditions

Achieves asymptotically minimal forecasting loss

Abstract

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 BuckleyCJames 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.