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Asymptotic properties of criteria for selection of variables in multiple regression. (English) Zbl 0544.62063
Summary: In normal linear regression analysis, many model selection rules proposed from various viewpoints are available. For the information criteria AIC, FPE, \(C_ p\), PSS and BIC, the asymptotic distribution of the selected model and the asymptotic quadratic risk based on each criterion are explicitly obtained.

MSC:
62J05 Linear regression; mixed models
62E20 Asymptotic distribution theory in statistics
62F12 Asymptotic properties of parametric estimators
62B10 Statistical aspects of information-theoretic topics
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