惩罚因素对订单选择标准的影响

P. Broersen, H. Wensink
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引用次数: 0

摘要

自回归模型阶数选择的目标是求预测误差最小的模型。选择次优阶的可能性可分为过拟合和欠拟合。在基于渐近大样本理论和有限样本理论的阶次选择准则中,惩罚因子/spl α /可以被认为是过拟合和欠拟合之间的平衡因子。只有在利用有限样本理论的结果对有限观测长度的统计量进行校正后,惩罚因子值的优化才有效。一种理论处理是基于真实AR过程顺序的渐近理论。为了将推理应用于实际情况,其中只有有限数量的观测值被测量,引入了最优模型顺序。它被定义为期望预测误差最小的阶数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The influence of the penalty factor in order selection criteria
The quest in autoregressive model order selection is for the model with smallest prediction error. The possibilities of selecting a suboptimal order can be divided in overfitting and underfitting. In order selection criteria based on asymptotical large sample theory as well as in their finite sample counterparts, the penalty factor /spl alpha/ can be considered as the balancing factor between overfit and underfit. An optimization of the value for the penalty factor is only effective, after a correction for the statistics of the finite observation length has been carried out, by using the results of the finite sample theory. A theoretical treatment is in asymptotic theory based on the true AR process order. To apply the reasonings to the practical situations, where only a finite number of observations has been measured, the optimal model order is introduced. It is defined as the order with lowest expected prediction error.<>
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