Boosted nonparametric hazards with time-dependent covariates

Given functional data samples from a survival process with time dependent covariates, we propose a practical 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. We use our boosting procedure to shed new light on a question from the operations literature concerning the effect of workload on service rates in an emergency department.