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Journal of Advanced Statistics
JAS > Volume 4, Number 1, March 2019

Consistency of the Semi-parametric MLE under the Cox Model with Linearly Time-dependent Covariates and Interval-censored Data

Download PDF  (345.3 KB)PP. 1-7,  Pub. Date:January 30, 2019
DOI: 10.22606/jas.2019.41001

Author(s)
Qiqing Yu*, Qinggang Diao
Affiliation(s)
Department of Mathematical Sciences, SUNY, Binghamton, NY 13902, USA
Abstract
Yu and Diao [1] studied the estimation problem under the Cox model with linearly time-dependent covariates and with interval-censored (IC) data under the distribution-free set-up. They proposed a modified semi-parametric MLE (MSMLE) and the simulation results suggest that the MSMLE is consistent. In this paper, we establish the consistency of the MSMLE.
Keywords
Cox’s model, time-dependent covariates, semi-parametric MLE, consistency.
References
  • [1]  Q.Q. Yu, and Q.G. Diao, “The Proportional Hazards Model with linearly time-dependent covariates and interval-censored data", Journal of Advanced Statistics vol. 3, no. 4, 58-70, 2018.
  • [2]  D.R. Cox, and D. Oakes, Analysis of Survival Data, Chapman & Hall, 1984.
  • [3]  A. Schick, and Q.Q. Yu, “Consistency of the GMLE with mixed case interval-censored data", Scandinavian Journal of Statistics, vol. 27, pp. 45-55, 2000.
  • [4]  P. Groeneboom, and J.A. Wellner, Information bounds and nonparametric maximum likelihood estimation, Birkh¨auser Verlag, Basel, 1992
  • [5]  G.Y.C. Wong, and Q.Q. Yu, “Estimation under the Lehmann regression model with interval-censored data", Communications in Statistics – Simulation and Computation, vol. 41, 1489-1500, 2012.
  • [6]  G.Y.C. Wong, Q.G. Diao, and Q.Q. Yu, “Piecewise proportional hazards models with interval-censored data", Journal of Statistical Computation and Simulation, vol. 88, pp.140-155, 2018.
  • [7]  H.L. Royden, Real Analysis, Second edition, New York: Macmillan, 1968.
  • [8]  W. F. Eddy, and J. A. Hartigan, “Uniform Convergence of the Empirical Distribution Function Over Convex Sets", The Annals of Statistics vol. 5, no. 2, pp. 370-374, 1977.
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