Given functional data samples from a survival process with time-dependent covariates, we propose a functional gradient boosting procedure for estimating its hazard function nonparametrically. The estimator is consistent if the model is correctly specified; alternatively an oracle inequality can be demonstrated for tree-based models. To avoid overfitting, boosting employs several regularization devices. One of them is step-size restriction, but the rationale for this is somewhat mysterious from the viewpoint of consistency. Our convergence bounds bring some clarity to this issue by revealing that step-size restriction is a mechanism for preventing the curvature of the risk from derailing convergence.
View on arXiv