## The Annals of Statistics

### Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set

Ker-Chau Li

#### Abstract

$C_p, C_L$, 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.

#### Article information

Source
Ann. Statist., Volume 15, Number 3 (1987), 958-975.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350486

Digital Object Identifier
doi:10.1214/aos/1176350486

Mathematical Reviews number (MathSciNet)
MR902239

Zentralblatt MATH identifier
0653.62037

JSTOR
Li, Ker-Chau. Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set. Ann. Statist. 15 (1987), no. 3, 958--975. doi:10.1214/aos/1176350486. https://projecteuclid.org/euclid.aos/1176350486