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Model selection with data-oriented penalty. (English) Zbl 0926.62045
Summary: We consider the problem of model (or variable) selection in the classical regression model using the GIC (general information criterion). In this method the maximum likelihood is used with a penalty function denoted by \(C_n\), depending on the sample size \(n\) and chosen to ensure consistency in the selection of the true model. There are various choices of \(C_n\) suggested in the literature on model selection. We show that a particular choice of \(C_n\) based on observed data, which makes it random, preserves the consistency property and provides improved performance over a fixed choice of \(C_n\).

MSC:
62J05 Linear regression; mixed models
62F10 Point estimation
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