Boosted Nonparametric Hazards with Time-Dependent Covariates

29 Pages Posted: 28 Jan 2017 Last revised: 25 Jun 2019

See all articles by Donald Lee

Donald Lee

Emory University - Goizueta Business School

Ningyuan Chen

University of Toronto at Mississauga - Department of Management; University of Toronto - Rotman School of Management

Hemant Ishwaran

University of Miami - Department of Epidemiology and Public Health

Date Written: February 12, 2017

Abstract

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

Suggested Citation

Lee, Donald and Chen, Ningyuan and Ishwaran, Hemant, Boosted Nonparametric Hazards with Time-Dependent Covariates (February 12, 2017). Available at SSRN: https://ssrn.com/abstract=2906586 or http://dx.doi.org/10.2139/ssrn.2906586

Donald Lee (Contact Author)

Emory University - Goizueta Business School ( email )

1300 Clifton Road
Atlanta, GA 30322-2722
United States

Ningyuan Chen

University of Toronto at Mississauga - Department of Management ( email )


Canada

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Hemant Ishwaran

University of Miami - Department of Epidemiology and Public Health ( email )

Miami, FL 33136
United States

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