cosso (version 2.1-0)

cosso.qr: Estimate the quantile function by Smoothing Splines with COSSO penalty

Description

Fit a penalized quantile regression model with COSSO regularization. The regularization path is computed for the COSSO penalty at a grid of values for the regularization parameter M.

Usage

cosso.qr(x,y,tau,wt=rep(1,ncol(x)),scale=FALSE,parallel=FALSE,cpus=1)

Arguments

x

input matrix; the number of rows is sample size, the number of columns is the data dimension. The range of input variables is scaled to [0,1].

y

response vector.

tau

the quantile to be estimated, a number strictly between 0 and 1.

wt

weights for predictors. Default is rep(1,ncol(x)).

scale

if TRUE, each predictor variable is rescaled to [0,1] interval. Dafault is FALSE.

parallel

parallelize task using snowfall package? Default is FALSE. Recommended when sample size is large.

cpus

number of available processor units. Default is 1.

Value

• An object with S3 class "cosso".
• family
  type of regression model.
• tau
  quantile to be estimated.
• wt
  weights.
• x
  input matrix.
• y
  response vector.
• basis.id
  Indices of observations used to compute the kernel matrices. All observations will be used in quantile regression.
• tune
  a list containing tuning result

Details

The quantile function is first assumed to have an additive form: $$\eta(x)=\sum_{j=1}^p\eta_j(x_j),$$ then estimated by minimizing the objective function: $$check~loss/nobs+\lambda_0\sum_{j=1}^p\theta^{-1}_jw_j^2||\eta_j||^2, s.t. \sum_{j=1}^p\theta_jKQRwt.

See Also

tune.cosso.qr, plot.cosso, predict.cosso

Examples

data(ozone)
t0 <- proc.time()
set.seed(27695)
## Use one third observations for demonstration
train_id   <- sample(1:nrow(ozone),round(nrow(ozone)/3))
cossoqrObj <- cosso.qr(x=ozone[train_id,2:5],y=ozone[train_id,1],tau=0.5)
print((proc.time()-t0)[3])

data(ozone)
## Parallel Computing
t0 <- proc.time()
set.seed(27695)
train_id   <- sample(1:nrow(ozone),round(nrow(ozone)/3))
cossoqrObj <- cosso.qr(x=ozone[train_id,2:9],y=ozone[train_id,1],tau=0.5,parallel=TRUE,cpus=2)
print((proc.time()-t0)[3])

data(ozone)
set.seed(27695)
train_id   <- sample(1:nrow(ozone),round(nrow(ozone)/3))
## Adaptive COSSO-QR
adaptive.wt <- KQRwt(ozone[train_id,2:9],ozone[train_id,1],0.5)
acossoqrObj <- cosso.qr(x=ozone[train_id,2:9],y=ozone[train_id,1],tau=0.5,wt=adaptive.wt)