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A class of cross-validatory model selection criteria. (English) Zbl 1294.62134
Summary: In this paper, we define a class of cross-validatory model selection criteria as an estimator of the predictive risk function based on a discrepancy between a candidate model and the true model. For a vector of unknown parameters, \(n\) estimators are required for the definition of the class, where \(n\) is the sample size. The \(i\)th estimator \((i=1,\dots,n)\) is obtained by minimizing a weighted discrepancy function in which the \(i\)th observation has a weight of \(1-\lambda\) and others have weight of 1. Cross-validatory model selection criteria in the class are specified by the individual \(\lambda\). The sample discrepancy function and the ordinary cross-validation (CV) criterion are special cases of the class. One may choose \(\lambda\) to minimize the biases. The optimal \(\lambda\) makes the bias-corrected CV (CCV) criterion a second-order unbiased estimator for the risk function, while the ordinary CV criterion is a first-order unbiased estimator of the risk function.
MSC:
62H25 Factor analysis and principal components; correspondence analysis
62F07 Statistical ranking and selection procedures
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