pocrepath {POCRE}

Build a POCRE Path for Different Values of Tuning Parameters

Description

Applying POCRE for a series of tuning parameters chosen by a pre-specified step size. The tuning parameter will increase until non-component can be constructed, and then decrease until a non-sparse regression is constructed (i.e., the number of non-zero coefficients in \beta is more than maxvar).

Usage

pocrepath(y, x, delta=0.1, maxvar=dim(x)[1]/2, x.nop=NA, maxcmp=10,
          ptype=c('ebtz','ebt','l1','scad','mcp'), lambda.init=1,
          maxit=100, tol=1e-6, maxtps=500, gamma=3.7, pval=(dim(y)[2]==1))

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).

delta

step size to increase or decrase from current tuning parameter.

maxvar

maximum number of selected variables.

x.nop

a vector indicating indices of covariates which are excluded only when evaluating the significance of components.

maxcmp

maximum number of components to be constructed.

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)).

lambda.init

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

maxit

maximum number of iterations to be allowed.

tol

tolerance of precision in iterations.

maxtps

maximum number of different values that the tuning parameter is allowed.

gamma

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

pval

a logical value indicating whether to calculate the p-values of components (not implemented for q>1, i.e., multiple response variables).

Value

A list of results from pocre, each for a specific 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 (2018). R package POCRE: Exploring high-dimensional data via supervised dimension reduction. Manuscript.

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

plot.pocrepath, selectmodel, pocre.

Examples

data(simdata)
xx <- simdata[,-1]
yy <- simdata[,1]

ppres <- pocrepath(yy,xx)