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

ABSTRACT

In 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.

KEYWORDS:

• Empirical likelihood
• penalised empirical likelihood
• high-dimensional censored data
• additive hazards model
• variable selection

Acknowledgments

We are grateful to the editor, the associate editor, and the referees for their insightful comments and suggestions which led to an improved presentation of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Project supported by Open Fund of Innovation Platform in Hunan province colleges and universities, 13k030.