An observation is removed and the model is fit the the remaining data and this fit used
to predict the value of the deleted observation.
This is repeated, n times, for each of the n observations and the mean square error
is computed.
Usage
LOOCV(X, y)
Arguments
X
training inputs
y
training output
Details
LOOCV for linear regression is exactly equivalent to the PRESS method
suggested by Allen (1971) who also provided an efficient algorithm.
Value
Vector of two components comprising the cross-validation MSE and its sd based on the MSE in
each validation sample.
Author(s)
A.I. McLeod and C. Xu
References
Hastie, T., Tibshirani, R. and Friedman, J. (2009).
The Elements of Statistical Learning. 2nd Ed.
Allen, D.M. (1971). Mean Square Error of Prediction as a Criterion for Selecting Variables.
Technometrics, 13, 469 -475.
See Also
bestglm,
CVd,
CVDH,
CVHTF
Examples
#Example. Compare LOO CV with K-fold CV.
#Find CV MSE's for LOOCV and compare with K=5, 10, 20, 40, 50, 60
#Takes about 30 sec
## Not run:
data(zprostate)
train<-(zprostate[zprostate[,10],])[,-10]
X<-train[,1:2]
y<-train[,9]
CVLOO<-LOOCV(X,y)
KS<-c(5,10,20,40,50,60)
nKS<-length(KS)
cvs<-numeric(nKS)
set.seed(1233211231)
for (iK in 1:nKS)
cvs[iK]<-CVDH(X,y,K=KS[iK],REP=10)[1]
boxplot(cvs)
abline(h=CVLOO, lwd=3, col="red")
title(sub="Boxplot of CV's with K=5,10,20,40,50,60 and LOO CV in red")
## End(Not run)