论文标题
使用新的稳健罚款术语在稳健回归中选择模型选择的信息复杂性标准
Information Complexity Criterion for Model Selection in Robust Regression Using A New Robust Penalty Term
论文作者
论文摘要
模型选择基本上是从模型子集中找到最佳模型的过程，其中解释变量对响应变量有效。缺乏拟合项的对数似然函数和指定的罚款项被用作模型选择标准中的两个部分。在本文中，我们得出了一种在鲁棒回归中选择模型选择的新工具。我们基于目标函数介绍了相对熵的新定义。由于分析的简单性，我们使用Huber的目标函数$ρ_H$，并提出我们指定的罚款项$ C_0^{ρ_H} $来得出新的信息复杂性标准（$ ricomp_ {C_0^{ρ_H}} $）作为强大的模型选择工具。此外，通过使用$ C_0^{ρ_H} $的属性，我们提出了一个新值的调整参数，称为$ K_ {C_0} $，用于Huber的$ρ_H$。如果存在对正常分布的污染，则$ ricomp_ {c_0^{ρ_H}} $比竞争对手更好地选择真实模型。进行了蒙特卡洛模拟研究，以显示$ k_ {c_0} $和$ ricomp_ {c_0^{ρ_H}} $的实用程序。还给出了一个真实的数据示例。
Model selection is basically a process of finding the best model from the subset of models in which the explanatory variables are effective on the response variable. The log likelihood function for the lack of fit term and a specified penalty term are used as two parts in a model selection criteria. In this paper, we derive a new tool for the model selection in robust regression. We introduce a new definition of relative entropy based on objective functions. Due to the analytical simplicity, we use Huber's objective function $ρ_H$ and propose our specified penalty term $C_0^{ρ_H}$ to derive new Information Complexity Criterion ($RICOMP_{C_0^{ρ_H}}$) as a robust model selection tool. Additionally, by using the properties of $C_0^{ρ_H}$, we propose a new value of tuning parameter called $k_{C_0}$ for the Huber's $ρ_H$. If a contamination to normal distribution exists, $RICOMP_{C_0^{ρ_H}}$ chooses the true model better than the rival ones. Monte Carlo Simulation studies are carried out to show the utility both of $k_{C_0}$ and $RICOMP_{C_0^{ρ_H}}$. A real data example is also given.
