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# 20th European Young Statisticians Meeting

14-18 August 2017
Uppsala University
Europe/Stockholm timezone

## Confidence regions in Cox proportional hazards model with measurement errors

17 Aug 2017, 16:00
30m
Ångströmslaboratoriet ()

Speaker

### 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)

### Presentation Materials

 Paper
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