Toma Aida, Karagrigoriou Alex, Trentou Paschalini
Department of Applied Mathematics, Bucharest University of Economic Studies, 010164 Bucharest, Romania.
"Gh. Mihoc - C. Iacob" Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 010164 Bucharest, Romania.
Entropy (Basel). 2020 Mar 6;22(3):304. doi: 10.3390/e22030304.
In this paper, we introduce a new class of robust model selection criteria. These criteria are defined by estimators of the expected overall discrepancy using pseudodistances and the minimum pseudodistance principle. Theoretical properties of these criteria are proved, namely asymptotic unbiasedness, robustness, consistency, as well as the limit laws. The case of the linear regression models is studied and a specific pseudodistance based criterion is proposed. Monte Carlo simulations and applications for real data are presented in order to exemplify the performance of the new methodology. These examples show that the new selection criterion for regression models is a good competitor of some well known criteria and may have superior performance, especially in the case of small and contaminated samples.
在本文中，我们引入了一类新的稳健模型选择准则。这些准则是通过使用伪距离的预期总体差异估计量和最小伪距离原则来定义的。证明了这些准则的理论性质，即渐近无偏性、稳健性、一致性以及极限定律。研究了线性回归模型的情况，并提出了一种基于特定伪距离的准则。为了例证新方法的性能，给出了蒙特卡罗模拟和实际数据应用。这些例子表明，回归模型的新选择准则是一些知名准则的有力竞争者，并且可能具有优越的性能，特别是在小样本和受污染样本的情况下。
