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Approximate efficiency of a selection procedure for the number of regression variables. (English) Zbl 0543.62053
An approximation to the regression mean squared error when the number of variables is selected through a minimum generalized final prediction error $$(FPE_{\alpha})$$ criterion is obtained. The evaluation proposed is exact if the probability of the selection procedure underestimating the number of variables is negligible. When this holds, an approximate efficiency of the selection procedure is suggested to be applied to choose $$\alpha$$. Finally, this approximate efficiency is used in a general situation to combine several procedures in a further generalization of $$FPE_{\alpha}$$.

##### MSC:
 62J05 Linear regression; mixed models
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