Journal of Advanced Statistics

Download PDF (345.3 KB) PP. 1 - 7 Pub. Date: March 1, 2019

DOI: 10.22606/jas.2019.41001

• Qiqing Yu^*, Qinggang Diao
  Department of Mathematical Sciences, SUNY, Binghamton, NY 13902, USA

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.

Cox’s model, time-dependent covariates, semi-parametric MLE, consistency.

[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.