论文标题
当尺寸增加时，在逻辑回归中被惩罚的鲁棒估计器的渐近行为
Asymptotic behaviour of penalized robust estimators in logistic regression when dimension increases
论文作者
论文摘要
以前已经对固定尺寸进行了研究，以获取稀疏的统计模型和自动变量选择，以前已经研究了logistic回归模型的罚款$ m- $估计器。在本文中，当尺寸$ p $随着样本量$ n $而增长时，我们将获得惩罚$ m $估计器的渐近结果。具体而言，我们获得了惩罚函数的某些选择的一致性和收敛结果速率。此外，我们证明这些估计器始终选择具有概率为1的变量并得出其渐近分布。
Penalized $M-$estimators for logistic regression models have been previously study for fixed dimension in order to obtain sparse statistical models and automatic variable selection. In this paper, we derive asymptotic results for penalized $M-$estimators when the dimension $p$ grows to infinity with the sample size $n$. Specifically, we obtain consistency and rates of convergence results, for some choices of the penalty function. Moreover, we prove that these estimators consistently select variables with probability tending to 1 and derive their asymptotic distribution.
