Boosted Nonparametric Hazards with Time-Dependent Covariates
29 Pages Posted: 28 Jan 2017 Last revised: 25 Jun 2019
Date Written: February 12, 2017
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.
Keywords: survival analysis; gradient boosting; functional data; step-size shrinkage; regression trees; likelihood functional; queuing transition rates; emergency departments
JEL Classification: C14, C24, C34, C41, C44, C53
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