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Estimation for counting processes with high-dimensional covariates

Abstract : We consider the problem of estimating the intensity of a counting process adjusted on high-dimensional covariates. We propose two different approaches. First, we consider a non-parametric intensity function and estimate it by the best Cox proportional hazards model given two dictionaries of functions. The first dictionary is used to construct an approximation of the logarithm of the baseline hazard function and the second to approximate the relative risk. In this high-dimensional setting, we consider the Lasso procedure to estimate simultaneously the unknown parameters of the best Cox model approximating the intensity. We provide non-asymptotic oracle inequalities for the resulting Lasso estimator. In a second part, we consider an intensity that rely on the Cox model. We propose two two-step procedures to estimate the unknown parameters of the Cox model. Both procedures rely on a first step which consists in estimating the regression parameter in high-dimension via a Lasso procedure. The baseline function is then estimated either via model selection or by a kernel estimator with a bandwidth selected by the Goldenshluger and Lepski method. We establish non-asymptotic oracle inequalities for the two resulting estimators of the baseline function. We conduct a comparative study of these estimators on simulated data, and finally, we apply the implemented procedure to a real dataset on breast cancer.
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Contributor : Sarah Lemler Connect in order to contact the contributor
Submitted on : Sunday, February 22, 2015 - 2:06:16 PM
Last modification on : Friday, February 5, 2021 - 4:12:04 PM
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  • HAL Id : tel-01119228, version 1



Sarah Lemler. Estimation for counting processes with high-dimensional covariates. Statistics [stat]. Universite d'Evry Val d'Essonne, 2014. English. ⟨tel-01119228⟩



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