Oracle inequalities for the Lasso for the conditional hazard rate in a high-dimensional setting

Sarah Lemler (1)

1 LSG - Laboratoire Statistique et Génome

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

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

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]; Applications [stat.AP]

Sarah Lemler. Oracle inequalities for the Lasso for the conditional hazard rate in a high-dimensional setting. 2012. ⟨hal-00710685v2⟩