Bernoulli

  • Bernoulli
  • Volume 23, Number 4B (2017), 3437-3468.

Efficiency and bootstrap in the promotion time cure model

François Portier, Anouar El Ghouch, and Ingrid Van Keilegom

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Abstract

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.

Article information

Source
Bernoulli, Volume 23, Number 4B (2017), 3437-3468.

Dates
Received: March 2015
Revised: January 2016
First available in Project Euclid: 23 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1495505098

Digital Object Identifier
doi:10.3150/16-BEJ852

Mathematical Reviews number (MathSciNet)
MR3654812

Zentralblatt MATH identifier
1384.62117

Keywords
asymptotic inference bootstrap Cox model promotion time cure model semiparametric efficiency

Citation

Portier, François; El Ghouch, Anouar; Van Keilegom, Ingrid. Efficiency and bootstrap in the promotion time cure model. Bernoulli 23 (2017), no. 4B, 3437--3468. doi:10.3150/16-BEJ852. https://projecteuclid.org/euclid.bj/1495505098


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