Oracle inequalities for the Lasso in the high-dimensional multiplicative Aalen intensity model

Sarah Lemler (1)

1 LSG - Laboratoire Statistique et Génome

We consider the problem of obtaining a prognostic on the survival time adjusted on covariates in a high-dimensional setting. Towards this end, we construct an estimator of the conditional intensity function that does not rely on an underlying model. We 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. As we are in high-dimension, we consider the Lasso procedure to estimate the unknown parameters of the best Cox model approximating the conditional hazard rate function. We provide non-asymptotic oracle inequalities for the Lasso estimator of the conditional hazard risk function. Our results rely on an empirical Bernstein's inequality for martingales with jumps.

Mots clés: Survival analysis; Right-censored data; Conditional hazard rate function; Cox proportional hazards model; Semiparametric model; Nonparametric model; High-dimensional covariates; Lasso; Non-asymptotic oracle inequalities; Empirical Bernstein's inequality

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Applications [stat.AP]

Sarah Lemler. Oracle inequalities for the Lasso in the high-dimensional multiplicative Aalen intensity model. 2013. ⟨hal-00710685v3⟩