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: 9202759
• 负责人: Chih-Ling Tsai
• 金额: $ 2.89万
• 依托单位: University of California-Davis
• 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 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9202759&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在线性回归和非回归时间序列分析中使用赤池信息标准（AICc）的修正和进一步改进的AICi版本的模型选择。由于大大减少了估计器对Kullback-Leibler差异的偏差，在所有情况下，模型选择性能都得到了实质性的小样本改进。研究人员建议在上述工作的基础上，为AICc建立一个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。统计学中的一个中心问题是从潜在的大量候选模型中选择一个合适的模型来应用于实际情况。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，有效决策过程的发展取决于决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少量观测数据选择模型的改进方法。