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Theory of Probability and Mathematical Statistics

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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).
Journal: Theor. Probability and Math. Statist. 82 (2011), 161-169
MSC (2010): Primary 62N01, 62N05, 62J12
Published electronically: August 5, 2011
MathSciNet review: 2790491
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the following accelerated failure time model used in the statistical analysis of the survival data:

$\displaystyle T_i=\exp\bigl\{\beta_0+\beta_X^T X_i+\varepsilon_i\bigr\}, \qquad i\geq 1.$

The lifetimes $ T_i$ are observed under censoring. We also observe the vectors $ W_i=X_i+U_i$ instead of the regressors $ X_i$, where the $ U_i$ are measurement errors. The vector of regression parameters $ \beta=\bigl(\beta_0,\beta_X^T\bigr)^T$ 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 $ X_i$ are bounded and the errors $ \varepsilon_i$ are bounded from above. For the latter case, we estimate the censoring distribution by the Kaplan-Meier method.

References [Enhancements On Off] (What's this?)

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Additional Information

O. S. Usoltseva
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

Keywords: Censoring, strong consistency, estimating function
Received by editor(s): November 30, 2009
Published electronically: August 5, 2011
Additional Notes: This research is supported by the Swedish Institute, grant SI-01424/2007
Article copyright: © Copyright 2011 American Mathematical Society