cv.hrq_glasso {hrqglas}

Cross-validation for quantile regression with group lasso

Description

K fold cross-validation is conducted. Four types of loss (squared error (se), absolute error (ae) quantile check loss (check) and huber loss (he)) can be specified as the CV criterion.

Usage

cv.hrq_glasso(
  x,
  y,
  group.index,
  tau = 0.5,
  k = 5,
  loss = "check",
  method = "quantile",
  folds = NULL,
  ...
)

Arguments

x

Design matrix

y

Response variable

group.index

A vector of group index, e.g., (1,1,1,2,2,2,3,3)

tau

Percentage

k

Number of folders.

loss

The loss function used for computing the cross-validation error. Supported losses include squared error (se), absolute error (ae), quantile check loss (check) and huber loss (he).

method

Choice for mean or quantile regression. Default is quantile.

folds

A vector of folder index for all observations. The procedure random splits if this argument is not specified.

...

Other inputs of function hrq_glasso().

Value

The full solution path is returned. It also returns the vector of CV score as well as the optimal values in terms of min and 1se. Corresponding lambda values are also returned.

beta

The estimated coefficients for all lambdas, stored in sparse matrix format, where each column corresponds to a lambda.

lambda

The sequence of lambdas.

lambda.min

The optimal lambda that minimizes the CV error

lambda.1se

The largest lambda such that CV error is within 1 standard error of the minimum CV error.

cv.all

The vector of all values of CV error for all lambdas.

cv.min

The value of CV error corresponding to lambda.min.

cv.1se

The value of CV error corresponding to lambda.1se.

folds

The vector of indices for k folds split.

cvup

CV error + 1 standard error

cvlo

CV error + 1 standard error

n.grp

The number of selected groups for each lambda.

Examples

n<- 100
p<- 10
x0<- matrix(rnorm(n*p),n,p)
X<- cbind(x0, x0^2, x0^3)[,order(rep(1:p,3))]
y<- -2+X[,1]+0.5*X[,2]-X[,3]-0.5*X[,7]+X[,8]-0.2*X[,9]+rt(n,2)
group<- rep(1:p, each=3)
fitcv<- cv.hrq_glasso(x=X, y=y, group.index=group, method="quantile")
plot(fitcv)