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Biometrika 1975 62(3):547-554; doi:10.1093/biomet/62.3.547
© 1975 by Biometrika Trust
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Goodness of prediction fit

J. AITCHISON

Department of Statistics, University of Glasgow

Fitting a parametric model or estimating a parametric density function plays an important role in a number of statistical applications. Two widely-used methods, one replacing the unknown parameter by an efficient estimate and so termed estimative and the other using a mixture of the possible density functions and commonly termed predictive, are compared. On a general criterion of closeness of fit based on a discriminating information measure the predictive method is shown to be preferable. Explicit measures of the relative closeness of predictive and estimative fits are obtained for gamma and multinomial models.

Key Words: Estimation of density functions • Goodness of fit • Predictive distributions


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