Mathematical Sciences: Regression and Time Series Model Selection in Small Samples

在最近的一系列论文中，主要研究人员探索了在线性回归和自回归时间序列分析中使用对Akaike信息标准AICC的修正和进一步改进的版本AICI进行模型选择。随着Kullback-Leibler偏差估计量的偏差大大降低，在所有情况下，模型选择性能的小样本都得到了实质性的改善。研究人员建议在上述工作的基础上，为AICC建立一个一般的理论和实践基础，因为它适用于时间序列和回归中的小样本模型选择问题。统计学中的一个中心问题是从潜在的一大类候选模型中选择一个合适的模型来应用于实际感兴趣的特定情况。选择不适当的模型可能会产生非常严重的后果：对未来事件的预测可能会严重扭曲和不准确，导致错误的决策和经济损失。因此，制定有效的决策过程取决于是否有能力决定哪种模型最适合手头的数据。研究人员建议开发和测试基于相当少量的观测数据选择模型的改进方法。

In a recent series of papers, the principal investigaors have explored the use of a correction to the Akaike Information Criterion, AICc, and a further-improved version AICi, for model selection in linear regression and artoregressive time series analysis. Substantial small-sample improvements in model selection performance are found in all cases as the bias of the estimator for Kullback-Leibler discrepancy is greatly reduced. The investigators propose to build on the above work by developing a general theoretical and pracitcal foundation for AICc as it applies to small-sample model selection problems in time series and regression. A central problem in statistics is that of selecting an appropriate model from a potentially large class of candidate models to apply in a particular situation of practical interest. The selection of an inadequate model can have very serious consequences: forecasts of future events may be substantially distorted and inaccurate, resulting in incorrect decisions, and financial losses. The development of an effective decision- making process therefore depends on the ability to decide which model seems best for the data at hand. The investigators propose to develop and test improved methods of selecting a model on the basis of a reasonably small amount of observed data.