Theory of Probability and Mathematical Statistics
Hypothesis testing in Cox proportional hazards model with measurement errors
O. O. Chernova
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Abstract: Cox proportional hazards model with measurement errors is considered, in which baseline hazard rate λ(·) belongs to a parameter set consisting of nonnegative Lipschitz functions, with fixed constant, and regression parameter β belongs to a compact parameter set. Censored lifetimes and regressors with additive errors are observed. Based on the simultaneous consistent estimator we construct statistics to test hypothesis about the regression parameter β and the integral functional of the baseline hazard rate λ(·). The consistency of the tests is obtained.
Keywords: Cox proportional hazards model, hypothesis testing, power of test, simultaneous estimation of baseline hazard rate and regression parameter.
Bibliography: 1. T. Augustin, An exact corrected log-likelihood function for Cox’s proportional hazards model under measurement error and some extensions, Scand. J. Stat., 31 (2004), no. 1, 43–50.
2. P. Billingsley, Convergence of probability measures, John Wiley & Sons, 2013.
3. H. Cartan, Differential Calculus, Hermann/Houghton Mifflin Co., Paris/Boston, MA, 1971.
4. O. Chernova, A. Kukush, Confidence regions in Cox proportional hazards model with measurement errors and unbounded parameter set, Mod. Stoch. Theory Appl., 5 (2018), no. 1, 37–52.
5. C. Chimisov, A. Kukush, Asymptotic normality of corrected estimator in Cox proportional hazards model with measurement error, Mod. Stoch. Theory Appl., 1 (2014), no. 1, 13–32.
6. A. Kukush, S. Baran, I. Fazekas, E. Usoltseva, Simultaneous estimation of baseline hazard rate and regression parameters in Cox proportional hazards model with measurement error, J. Statist. Res., 45 (2011), no. 2, 77–94.
7. A. Kukush, O. Chernova, Consistent estimation in Cox proportional hazards model with measurement errors and unbounded parameter set. Theor. Probability and Math. Statist., 96 (2018), 101–110.
8. A. Kukush, O. Chernova, Goodness-of-fit test in Cox proportional hazards model with measurement errors, Teor. Imovir. Mat. Stat., 99 (2018), 113–122. (Ukrainian)
