| tilting {tilting} | R Documentation |
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. |
Author(s)
Haeran Cho
References
H. Cho and P. Fryzlewicz (2012) High-dimensional variable selection via tilting, Journal of the Royal Statistical Society Series B, 74: 593-622.
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