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Biometrika 1996 83(1):41-54; doi:10.1093/biomet/83.1.41
© 1996 by Biometrika Trust
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Generalised linear model selection by the predictive least quasi-deviance criterion

GUOQI QIAN, GEORGE GABOR and R. P. GUPTA

Department of Mathematics, Statistics and Computing Science, Dalhousie University Halifax, Nova Scotia B3H 3J5, Canada

We consider the problem of selecting a model with the best predictive ability in a class of generalised linear models. A predictive least quasi-deviance criterion is proposed to measure the predictive ability of a model. This criterion is obtained by applying the idea of the predictive minimum description length principle and the theory of quasi-likelihood functions. The resulting predictive quasi-deviance function is an extension of the predictive stochastic complexity of the model. Under rather weak conditions the predictive least quasi-deviance method is shown to be consistent in the sense that the probability of selecting the right model converges to one as the number of observations goes to infinity. Also we show that the selected model converges to the optimal model in expectation. The method is then modified for finite sample applications. Examples and simulation results are presented.

Key Words: Consistency • Model selection • Prediction • Predictive least quasi-deviance • Predictive stochastic complexity • Prequential analysis • Quasi-likelihood function


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