Spline regression for hazard rate estimation when data are censored and measured with error |
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| Authors: | Fabienne Comte Gwennaelle Mabon Adeline Samson |
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| Affiliation: | 1. MAP5, UMR CNRS 8145, Université Paris Descartes, France;2. CREST ‐ ENSAE, Malakoff, France;3. Laboratoire Jean Kuntzmann, UMR CNRS 5224, Université Grenoble‐Alpes, France |
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| Abstract: | In this paper, we study an estimation problem where the variables of interest are subject to both right censoring and measurement error. In this context, we propose a nonparametric estimation strategy of the hazard rate, based on a regression contrast minimized in a finite‐dimensional functional space generated by splines bases. We prove a risk bound of the estimator in terms of integrated mean square error and discuss the rate of convergence when the dimension of the projection space is adequately chosen. Then we define a data‐driven criterion of model selection and prove that the resulting estimator performs an adequate compromise. The method is illustrated via simulation experiments that show that the strategy is successful. |
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| Keywords: | censored data measurement error nonparametric methods deconvolution B‐spline |
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