Based on the expectile loss function and the adaptive LASSO penalty, the paper proposes and studies the estimation methods for the accelerated failure time (AFT) model. In this approach, we need to estimate the survival function of the censoring variable by the Kaplan-Meier estimator. The AFT model parameters are first estimated by the expectile method and afterwards, when the number of explanatory variables can be large, by the adaptive LASSO expectile method which directly carries out the automatic selection of variables. We also obtain the convergence rate and asymptotic normality for the two estimators, while showing the sparsity property for the censored adaptive LASSO expectile estimator. A numerical study using Monte Carlo simulations confirms the theoretical results and demonstrates the competitive performance of the two proposed estimators. The usefulness of these estimators is illustrated by applying them to three survival data sets.

翻译：本文基于期望分位数损失函数与自适应LASSO惩罚，提出并研究了加速失效时间模型的估计方法。在该方法中，我们采用Kaplan-Meier估计量估计删失变量的生存函数。首先通过期望分位数法估计AFT模型参数，随后在解释变量数量可能较大的情况下，采用自适应LASSO期望分位数法直接实现变量的自动选择。本文还推导了两种估计量的收敛速度与渐近正态性，并证明了删失数据下的自适应LASSO期望分位数估计量具有稀疏性。通过蒙特卡洛模拟的数值研究验证了理论结果，并展示了两种估计量的竞争性能。最后，将估计量应用于三个生存数据集，进一步说明了其实用价值。