tilting (version 1.1)

tilting: Variable selection via Tilted Correlation Screening algorithm

Description

Given a design matrix and a response vector, the function selects a threshold for the sample correlation matrix, computes an adaptive measure for the contribution of each variable to the response variable based on the thus-thresholded sample correlation matrix, and chooses a variable at each iteration. Once variables are selected in the "active" set, the extended BIC is used for the final model selection.

Usage

tilting(X, y, thr.step = NULL, thr.rep = 1, max.size = NULL, max.count = NULL, 
op = 2, bic.gamma = 1, eps = 1e-10)

Arguments

X

design matrix.

y

response vector.

thr.step

a step size used for threshold selection. When thr.step==NULL, it is chosen automatically.

thr.rep

the number of times for which the threshold selection procedure is repeated.

max.size

the maximum number of the variables conditional on which the contribution of each variable to the response is measured (when max.size==NULL, it is set to be half the number of observations).

max.count

the maximum number of iterations.

op

when op==1, rescaling 1 is used to compute the tilted correlation. If op==2, rescaling 2 is used.

bic.gamma

a parameter used to compute the extended BIC.

eps

an effective zero.

Value

active

active set containing the variables selected over the iterations.

thr.seq

a sequence of thresholds selected over the iterations.

bic.seq

extended BIC computed over the iterations.

active.hat

finally chosen variables using the extended BIC.

References

H. Cho and P. Fryzlewicz (2011) "High-dimensional variable selection via tilting".

Examples

X<-matrix(rnorm(100*100), 100, 100) # 100-by-100 design matrix
y<-apply(X[,1:5], 1, sum)+rnorm(100) # first five variables are significant

tilt<-tilting(X, y, op=2)
tilt$active.hat # returns the finally selected variables