论文标题
抗否定的信息标准的多元扩展
A multivariate extension of the Misspecification-Resistant Information Criterion
论文作者
论文摘要
在[H.-L。中提出的不指定性信息标准（MRIC）。 HSU，C.-K。 Ing，H。Tong：从有限指定的时间序列模型的有限家族中选择模型。统计年鉴。 47（2），1061--1087（2019）]是单变量参数时间序列的模型选择标准，既享有一致性和渐近效率的属性。在本文中，我们将MRIC扩展到响应是多变量时间序列并且预测因子是单变量的情况。扩展需要基于随机矩阵理论的新衍生。我们获得了平方平方预测误差矩阵，即矢量mRIC的渐近表达，并证明了其运动方法估计器的一致性。此外，我们证明了其渐近效率。最后，我们以一个例子为例，在存在错误指定的情况下，矢量MRIC确定了最佳的预测模型，而传统的信息标准（例如AIC或BIC）未能实现这一任务。
The Misspecification-Resistant Information Criterion (MRIC) proposed in [H.-L. Hsu, C.-K. Ing, H. Tong: On model selection from a finite family of possibly misspecified time series models. The Annals of Statistics. 47 (2), 1061--1087 (2019)] is a model selection criterion for univariate parametric time series that enjoys both the property of consistency and asymptotic efficiency. In this article we extend the MRIC to the case where the response is a multivariate time series and the predictor is univariate. The extension requires novel derivations based upon random matrix theory. We obtain an asymptotic expression for the mean squared prediction error matrix, the vectorial MRIC and prove the consistency of its method-of-moments estimator. Moreover, we prove its asymptotic efficiency. Finally, we show with an example that, in presence of misspecification, the vectorial MRIC identifies the best predictive model whereas traditional information criteria like AIC or BIC fail to achieve the task.
