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Significance Tests for Regression Model Hierarchies

T. P. BarnettClimate Research Group, Scripps Institution of Oceanography, La Jolla, CA 92093

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R. W. PreisendorferClimate Research Group, Scripps Institution of Oceanography, La Jolla, CA 92093

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L. M. GoldsteinClimate Research Group, Scripps Institution of Oceanography, La Jolla, CA 92093

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K. HasselmannClimate Research Group, Scripps Institution of Oceanography, La Jolla, CA 92093

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Abstract

Methods of estimating the significance of optimal regression models selected from a model hierarchy proposed by Barnett and Hasselmann (1979) are reexamined allowing for the multiple-candidate nature of the selection criteria. It is found that the single-candidate models' significance value previously used can over- or underestimate the true multiple-candidate significance level of the selected model depending on the selection criteria used. A number of possible selection strategies to remove these problems are discussed and evaluated both theoretically and by Monte Carlo simulators.

Abstract

Methods of estimating the significance of optimal regression models selected from a model hierarchy proposed by Barnett and Hasselmann (1979) are reexamined allowing for the multiple-candidate nature of the selection criteria. It is found that the single-candidate models' significance value previously used can over- or underestimate the true multiple-candidate significance level of the selected model depending on the selection criteria used. A number of possible selection strategies to remove these problems are discussed and evaluated both theoretically and by Monte Carlo simulators.

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