Open Access
November 2017 Efficiency and bootstrap in the promotion time cure model
François Portier, Anouar El Ghouch, Ingrid Van Keilegom
Bernoulli 23(4B): 3437-3468 (November 2017). DOI: 10.3150/16-BEJ852


In this paper, we consider a semiparametric promotion time cure model and study the asymptotic properties of its nonparametric maximum likelihood estimator (NPMLE). First, by relying on a profile likelihood approach, we show that the NPMLE may be computed by a single maximization over a set whose dimension equals the dimension of the covariates plus one. Next, using $Z$-estimation theory for semiparametric models, we derive the asymptotics of both the parametric and nonparametric components of the model and show their efficiency. We also express the asymptotic variance of the estimator of the parametric component. Since the variance is difficult to estimate, we develop a weighted bootstrap procedure that allows for a consistent approximation of the asymptotic law of the estimators. As in the Cox model, it turns out that suitable tools are the martingale theory for counting processes and the infinite dimensional $Z$-estimation theory. Finally, by means of simulations, we show the accuracy of the bootstrap approximation.


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François Portier. Anouar El Ghouch. Ingrid Van Keilegom. "Efficiency and bootstrap in the promotion time cure model." Bernoulli 23 (4B) 3437 - 3468, November 2017.


Received: 1 March 2015; Revised: 1 January 2016; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 1384.62117
MathSciNet: MR3654812
Digital Object Identifier: 10.3150/16-BEJ852

Keywords: asymptotic inference , bootstrap , Cox model , promotion time cure model , Semiparametric efficiency

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 4B • November 2017
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