A consistent estimator in the accelerated failure time model with censored observations and measurement errors
Author:O. S. Usoltseva Translated by:S. Kvasko Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Theor. Probability and Math. Statist. 82 (2011), 161-169
Primary 62N01, 62N05, 62J12
August 5, 2011
MathSciNet review:2790491 Full-text PDF
Abstract: We consider the following accelerated failure time model used in the statistical analysis of the survival data:
The lifetimes are observed under censoring. We also observe the vectors instead of the regressors , where the are measurement errors. The vector of regression parameters is estimated from the observations. We construct an estimator as a solution of the corresponding unbiased estimating equation and show that this estimator is consistent if the censoring distribution is known. We also prove the consistency of the estimators for the case of an unknown censoring distribution if the regressors are bounded and the errors are bounded from above. For the latter case, we estimate the censoring distribution by the Kaplan-Meier method.
T. Augustin, Survival Analysis under Measurement Error, Habilitationsschrift, Universität München, 2002.
O. S. Usoltseva Affiliation:
Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine