cvpocre {POCRE}

Use k-Fold Cross-Validation to Choose the Tuning Parameter for POCRE

Description

Choose the optimal tuning parameter via k-fold cross-validation for POCRE.

Usage

cvpocre(y, x, n.folds=10, delta=0.1, maxvar=dim(x)[1]/2,
        ptype=c('ebtz','ebt','l1','scad','mcp'), maxit=100,
        maxcmp=10, gamma=3.7, lambda.init=1, tol=1e-6,
        crit=c('press','Pearson','Spearman','Kendall'))

Arguments

y

n*q matrix, values of q response variables (allow for multiple response variables).

x

n*p matrix, values of p predicting variables (excluding the intercept).

n.folds

number of folds to split the data (10-fold CV by default).

delta

step size of different values of the tuning parameter.

maxvar

maximum number of selected variables.

ptype

a character to indicate the type of penalty: 'ebtz' (emprical Bayes thresholding after Fisher's z-transformation, by default), 'ebt' (emprical Bayes thresholding by Johnstone & Silverman (2004)), 'l1' (L_1 penalty), 'scad' (SCAD by Fan & Li (2001)), 'mcp' (MCP by Zhang (2010)).

maxit

maximum number of iterations to be allowed.

maxcmp

maximum number of components to be constructed.

gamma

a parameter used by SCAD and MCP (=3.7 by default).

lambda.init

initial value of the tuning parameter (=1 by default).

tol

tolerance of precision in iterations.

crit

a character to indicate the validation criterion: 'press' (prediction residual error sum of squares, by default), 'Pearson' (Pearson correlation coefficient), 'Spearman' (Spearman's rank correlation coefficient), 'Kendall' (Kendall's rank correlation coefficient).

Details

Use k-folds cross-validation to find the optinal value for the tuning parameter. The validation criterion can be chosen from PRESS, or different types of correlation coefficients, such as Pearson's, Spearman's, or Kendall's.

Value

The optimal value of the tuning parameter.

Author(s)

Dabao Zhang, Zhongli Jiang, Zeyu Zhang, Department of Statistics, Purdue University

References

Fan J and Li R (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96:1348-1360

Johnstone IM and Silverman BW (2004). Needles and straw in haystacks: empirical Bayes estimates of possibly sparse sequences. Annals of Statistics, 32: 1594-1649.

Zhang C-H (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38: 894-942.

Zhang D, Lin Y, and Zhang M (2009). Penalized orthogonal-components regression for large p small n data. Electronic Journal of Statistics, 3: 781-796.

See Also

pocrescreen, pocrepath, pocre.

Examples

## Not run: 
data(simdata)
n <- dim(simdata)[1]
xx <- simdata[,-1]
yy <- simdata[,1]

# tp <- cvpocre(yy,xx,delta=0.01)
tp <- cvpocre(yy,xx)
print(paste("  pocre: Optimal Tuning Parameter = ", tp))
cvpres <- pocre(yy,xx,lambda=tp,maxvar=n/log(n))

## End(Not run)