Summary
A model selection rule of the form minimize [−2 log (maximized likelihood)+complexity] is considered, which is equivalent to Akaike's minimum AIC rule if the complexity of a model is defined to be twice the number of independently adjusted parameters of the model. Under reasonable assumptions, when applied to a locally asymptotically normal sequence of experiments, the model selection rule is shown to be locally asymptotically admissible with respect to a loss function of the form [inaccuracy+complexity], where the inaccuracy is defined as twice the Kullback-Leibler measure of the discrepancy between the true model and the fitted version of the selected model.
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This research was supported by NSF Grant No. MCS 80-02732.
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Stone, C.J. Local asymptotic admissibility of a generalization of Akaike's model selection rule. Ann Inst Stat Math 34, 123–133 (1982). https://doi.org/10.1007/BF02481014
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DOI: https://doi.org/10.1007/BF02481014