Penalised empirical likelihood for the additive hazards model with high-dimensional data

Abstract

ABSTRACTIn this article, we apply the empirical likelihood (EL) method to the additive hazards model with high-dimensional data and propose the penalised empirical likelihood (PEL) method for parameter estimation and variable selection. It is shown that the estimator based on the EL method has the efficient property, and the limit distribution of the EL ratio statistic for the parameters is a asymptotic normal distribution under the true null hypothesis. In a high-dimensional setting, we prove that the PEL method in the additive hazards model has the oracle property, that is, with probability tending to 1, and the estimator based on the PEL method for the nonzero parameters is estimation and selection consistent if the hypothesised model is true. Moreover, the PEL ratio statistic for the parameters is a distribution under the true null hypothesis. The performance of the proposed methods is illustrated via a real data application and numerical simulations.