Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set
Li, Ker-Chau
Ann. Statist., Tome 15 (1987) no. 1, p. 958-975 / Harvested from Project Euclid
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$C_p, C_L$, cross-validation and generalized cross-validation are useful data-driven techniques for selecting a good estimate from a proposed class of linear estimates. The asymptotic behaviors of these procedures are studied. Some easily interpretable conditions are derived to demonstrate the asymptotic optimality. It is argued that cross-validation and generalized cross-validation can be viewed as some special ways of applying $C_L$. Applications in nearest-neighbor nonparametric regression and in model selection are discussed in detail.
Publié le : 1987-09-14
Classification:  Model-selection,  nearest-neighbor estimates,  nil-trace linear estimates,  nonparametric regression,  Stein estimates,  Stein's unbiased risk estimates,  62G99,  62J99,  62J05,  62J07 
@article{1176350486,
     author = {Li, Ker-Chau},
     title = {Asymptotic Optimality for $C\_p, C\_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set},
     journal = {Ann. Statist.},
     volume = {15},
     number = {1},
     year = {1987},
     pages = { 958-975},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350486}
}

Li, Ker-Chau. Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set. Ann. Statist., Tome 15 (1987) no. 1, pp.  958-975. http://gdmltest.u-ga.fr/item/1176350486/