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題名 | An Asymptotic Theory for Linear Model Selection |
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作者姓名(外文) | Shao,Jun; | 書刊名 | Statistica Sinica |
卷期 | 7:2 1997.04[民86.04] |
頁次 | 頁221-264 |
分類號 | 319.5 |
關鍵詞 | 漸近理論; 線性模式選取; C抅; AIC; Asymptotic loss efficiency; BIC; Consistency; Crossvalidation; GIC; Squared error loss; |
語文 | 英文(English) |
英文摘要 | In the problem of selecting a linear model to approximate the true unknown regression model, some necessary and/or sufficient conditions are established for the asymptotic validity of various model selection procedures such as Akaike's AIC, Mallows' C[9064], Shibata's FPE[90b5], Schwarz' BIC, generalized AIC, cross-validation, and generalized cross-validation. It is found that these selection procedures can be classified into three classes according to their asymptotic behavior. Under some fairly weak conditions, the selection procedures in one class are asymptotically valid if there exist fixed-dimension correct models; the selection procedures in another class are asymptotically valid if no fixed-dimension correct model exists. The procedures in the third class are compromises of the procedures in the first two classes. Some empirical results are also presented. |
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