Description Usage Arguments Details Value References Examples
Draw guassian bootstrap or wild multiplier bootstrap samples to derive the lasso estimator along with its subgradient.
1 2 3 4 
X 
predictor matrix. 
PE_1, sig2_1, lbd_1 
parameters of target distribution.
(point estimate of beta or 
PE_2, sig2_2, lbd_2 
additional parameters of target distribution. This is required only if mixture distribution is used. 
weights 
weight vector with length equal to the number of groups. Default is

group 

niter 
integer. The number of iterations. Default is 
type 
type of penalty. Must be specified to be one of the following:

PEtype 
Type of 
Btype 
Type of bootstrap method. Users can choose either 
Y 
response vector. This is only required when 
parallel 
logical. If 
ncores 
integer. The number of cores to use for parallelization. 
verbose 
logical. This works only when

This function provides bootstrap samples for lasso, group lasso,
scaled lasso or scaled group lasso estimator
and its subgradient.
The sampling distribution is chracterized by (PE, sig2, lbd)
.
If Btype = "gaussian"
, error_new
is generated from N(0, sig2)
.
If Btype = "wild"
, we further multiply error_new
with the residuals.
Then, if PEtype = "coeff"
, y_new
is generated by X * PE + error_new
and if PEtype = "mu"
, y_new
is PE + error_new
.
By providing (PE_2, sig2_2, lbd_2)
, users can use a mixture sampling distribution.
In 1/2 probability, samples will be drawn from the distribution with parameters
(PE_1, sig2_1, lbd_1) and with another 1/2 probability, they will be drawn from
the distribution with parameters (PE_2, sig2_2, lbd_2).
Four distict penalties can be used; "lasso"
for lasso, "grlasso"
for group lasso,
"slasso"
for scaled lasso and "sgrlasso"
for scaled group lasso.
See Zhou(2014) and Zhou and Min(2016) for details.
beta 
coefficient estimate. 
subgrad 
subgradient. 
hsigma 
standard deviation estimator, for type="slasso" or type="sgrlasso" only. 
X, PE, sig2, weights, group, type, PEtype, Btype, Y, mixture 
model parameters. 
Zhou, Q. (2014), "Monte Carlo simulation for Lassotype problems by estimator augmentation," Journal of the American Statistical Association, 109, 14951516.
Zhou, Q. and Min, S. (2017), "Estimator augmentation with applications in highdimensional group inference," Electronic Journal of Statistics, 11(2), 30393080.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  set.seed(1234)
n < 10
p < 30
Niter < 10
Group < rep(1:(p/10), each = 10)
Weights < rep(1, p/10)
x < matrix(rnorm(n*p), n)
#
# Using nonmixture distribution
#
PBsampler(X = x, PE_1 = rep(0, p), sig2_1 = 1, lbd_1 = .5,
weights = Weights, group = Group, type = "grlasso", niter = Niter, parallel = FALSE)
PBsampler(X = x, PE_1 = rep(0, p), sig2_1 = 1, lbd_1 = .5,
weights = Weights, group = Group, type = "grlasso", niter = Niter, parallel = TRUE)
#
# Using mixture distribution
#
PBsampler(X = x, PE_1 = rep(0, p), sig2_1 = 1, lbd_1 = .5,
PE_2 = rep(1, p), sig2_2 = 2, lbd_2 = .3, weights = Weights,
group = Group, type = "grlasso", niter = Niter, parallel = TRUE)

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