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Theory of Probability and Mathematical Statistics

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Goodness-of-fit test in the Cox proportional hazards model with measurement errors


Authors: A. G. Kukush and O. O. Chernova
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 99 (2018).
Journal: Theor. Probability and Math. Statist. 99 (2019), 125-135
MSC (2010): Primary 62N03; Secondary 62N01
DOI: https://doi.org/10.1090/tpms/1085
Published electronically: February 27, 2020
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Abstract: We consider the Cox proportional hazards model whose baseline hazard function $ \lambda (\boldsymbol {\cdot })$ belongs to the parameter set consisting of nonnegative functions satisfying the Lipschitz condition and whose regression vector of coefficients $ \beta $ belongs to a compact parameter set. The censored lifetime and corresponding values of regressors perturbed by the classical additive measurement error are observed. A goodness-of-fit test is constructed on the base of the strongly consistent simultaneous estimator of  $ \lambda (\boldsymbol {\cdot })$ and $ \beta $ introduced in the paper by Kukush and Chernova [Teor. Imovir. Mat. Stat. 96 (2017), pp. 100-109]. The test statistic has the asymptotic chi-square distribution under the null hypothesis. The power of the test is found for corresponding local alternatives.


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

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Additional Information

A. G. Kukush
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, Taras Schevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: alexander_kukush@univ.kiev.ua

O. O. Chernova
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Taras Schevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: chernovaoksan@gmail.com

DOI: https://doi.org/10.1090/tpms/1085
Keywords: Consistent estimator, goodness-of-fit test, local alternatives, Cox proportional hazards model, power of a test, joint estimation of the baseline hazard function and regression parameter
Received by editor(s): July 31, 2018
Published electronically: February 27, 2020
Article copyright: © Copyright 2020 American Mathematical Society