R: Cross-validation using delete-d method.

CVd {bestglm} | R Documentation

## Cross-validation using delete-d method.

### Description

The delete-d method for cross-validation uses a random sample of d observations as the validation sample. This is repeated many times.

### Usage

    CVd(X, y, d = ceiling(n * (1 - 1/(log(n) - 1))), REP = 100, family = gaussian, ...)

### Arguments

`X` | training inputs
`y` | training output
`d` | size of validation sample
`REP` | number of replications
`family` | glm family
`...` | optional arguments passed to `glm` or `lm`

### Details

Shao (1993, 1997) suggested the delete-d algorithm implemented in this function. In this algorithm, a random sample of d observations are taken as the validation sample. This random sampling is repeated `REP` times. Shao (1997, p.234, eqn. 4.5 and p.236) suggests d= n(1-1/(log n - 1)), This is obtained by taking λ_n = log n on page 236 (Shao, 1997). As shown in the table Shao's recommended choice of the d parameter corresponds to validation samples that are typically much larger that used in 10-fold or 5-fold cross-validation. LOOCV corresponds to d=1 only!

n | d | K=10 | K=5
50 | 33 | 5 | 10
100 | 73 | 10 | 20
200 | 154 | 20 | 40
500 | 405 | 50 | 100
1000 | 831 | 100 | 200

### 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

Shao, Jun (1993). Linear Model Selection by Cross-Validation. Journal of the American Statistical Assocation 88, 486-494.

Shao, Jun (1997). An Asymptotic Theory for Linear Model Selection. Statistica Sinica 7, 221-264.

### See Also

`bestglm`, `CVHTF`, `CVDH`, `LOOCV`

### Examples

    #Example 1. delete-d method
    #For the training set, n=67. So 10-fold CV is like using delete-d
    #with d=7, approximately.
    data(zprostate)
    train<-(zprostate[zprostate[,10],])[,-10]
    X<-train[,1:2]
    y<-train[,9]
    set.seed(123321123)
    CVd(X, y, d=7, REP=10)
    #should set to 1000. Used 10 to save time in example.

[Package bestglm version 0.36 Index]