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

数学科学：小样本中的回归和时间序列模型选择

• 批准号: 9203347
• 负责人: Clifford Hurvich
• 金额: $ 3.1万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203347&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Regression; Time; Series

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.

在最近的一系列论文中，主要研究人员探索了使用赤池信息准则的修正 AICc 和进一步改进的 AICi 版本来进行线性回归和自回归时间序列分析中的模型选择。 在所有情况下，随着 Kullback-Leibler 差异估计量的偏差大大降低，模型选择性能都得到了显着的小样本改进。 研究人员建议在上述工作的基础上，为 AICc 建立通用的理论和实践基础，因为它适用于时间序列和回归中的小样本模型选择问题。 统计学的一个中心问题是从潜在的一大类候选模型中选择合适的模型以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，从而导致错误的决策和财务损失。 因此，有效决策过程的发展取决于确定哪种模型最适合手头数据的能力。 研究人员建议开发和测试基于相当少量的观察数据选择模型的改进方法。