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

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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.