sipocre: Penalized Orthogonal-Components Regression (POCRE) with...

In POCRE: Penalized Orthogonal-Components Regression

Penalized Orthogonal-Components Regression (POCRE) with Significance Inference

Description

Applying POCRE to select variables and evaluate the significance of selected variables using the multiple splitting method by Meinshausen et al. (2009). The tuning parameter may be selected based on either an information criterion or k-fold cross-validation. The tuning parameter can also be fixed at a prespecified value.

Usage

sipocre(y, x, n.splits=10, delta=0.1, crit=c('ic','cv','fixed'),
        ptype=c('ebtz','ebt','l1','scad','mcp'), maxvar=dim(x)[1]/2,
        msc=NA, maxit=100, maxcmp=50, gamma=3.7, tol=1e-6,
        n.folds=10, lambda=1, n.train=round(nrow(x)/2))

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.splits	number of random splits (=10 by default).
delta	step size to increase or decrase from current tuning parameter.
crit	character indicating the criterion to choose the tuning parameter: 'ic' (information criteria such as AIC, AICc, BIC, EBIC), 'cv' (k-folds cross-valdiation) or 'fixed' (a pre-specified value).
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)).
maxvar	maximum number of selected variables.
msc	value(s) to indicate the penalty related to the information criterion: 0~1 for (E)BIC, 2 for AIC, 3 for AICc, used when crit='ic'.
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).
tol	tolerance of precision in iterations.
n.folds	number of folds in k-folds cross-validation, used when crit='cv'.
lambda	pre-sepcified value for the tuning parameter, used when crit='fixed'.
n.train	sample size of the training data set.

Value

a list consisting of the following components,

cpv	component-based p-values which are calculated by testing the constructed components, either a matrix (when crit='ic', in this case each column corresponds to one value in msc) or a vector (when crit='cv' or crit='fixed').
xpv	traditional p-values, either a matrix (when crit='ic', in this case each column corresponds to one value in msc) or a vector (when crit='cv' or crit='fixed').

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.

Meinshausen N, Meier L, and Buhlmann P (2009) p-Values for High-Dimensional Regression. Journal of the American Statistical Association, 104: 1671-1681.

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

pocre.

Examples

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

sipres <- sipocre(yy,xx)

## End(Not run)

POCRE documentation built on March 18, 2022, 6:43 p.m.