Speaker
Ms
Oksana Chernova
(Taras Shevchenko National University of Kyiv)
Description
Cox proportional hazards model with measurement errors in covariates is considered. It is the ubiquitous technique in biomedical data analysis. In Kukush et al. (2011) [ Journal of Statistical Research **45**, 77-94 ] and Chimisov and Kukush (2014) [ Modern Stochastics: Theory and Applications **1**, 13-32 ] asymptotic properties of a simultaneous estimator $(\lambda_n;\beta_n)$ for the baseline hazard rate $\lambda(\cdot)$ and the regression parameter $\beta$ were studied, at that the parameter set $\Theta=\Theta_{\lambda}\times \Theta_{\beta}$ was assumed bounded.
In Kukush and Chernova (2017) [ Theory of Probability and Mathematical Statistics **96**, 100-109 ] we dealt with the simultaneous estimator $(\lambda_n;\beta_n)$ in the case, where the $\Theta_{\lambda}$ was unbounded from above and not separated away from $0$. The estimator was constructed in two steps: first we derived a strongly consistent estimator and then modified it to provide its asymptotic normality.
In this talk, we construct the confidence interval for an integral functional of $\lambda(\cdot)$ and the confidence region for $\beta$. We reach our goal in each of the three cases: (a) the measurement error is bounded, (b) it is normally distributed, or (c) it is a shifted Poisson random variable. The censor is assumed to have a continuous pdf. In future research we intend to elaborate a method for heavy tailed error distributions.
Primary author
Ms
Oksana Chernova
(Taras Shevchenko National University of Kyiv)
