qic.select.rq.pen.seq: Select tuning parameters using IC

In rqPen: Penalized Quantile Regression

Select tuning parameters using IC

Description

Selects tuning parameter \lambda and a according to information criterion of choice. For a given \hat{\beta} the information criterion is calculated as

\log(\sum_{i=1}^n w_i \rho_\tau(y_i-x_i^\top\hat{\beta})) + d*b/(2n),

where d is the number of nonzero coefficients and b depends on the method used. For AIC b=2, for BIC b=log(n) and for PBIC d=log(n)*log(p) where p is the dimension of \hat{\beta}. If septau set to FALSE then calculations are made across the quantiles. Let \hat{\beta}^q be the coefficient vector for the qth quantile of Q quantiles. In addition let d_q and b_q be d and b values from the qth quantile model. Note, for all of these we are assuming eqn and a are the same. Then the summary across all quantiles is

\sum_{q=1}^Q w_q[ \log(\sum_{i=1}^n \rho_\tau(y_i-x_i^\top\hat{\beta}^q)) + d_q*b_q/(2n)],

where w_q is the weight assigned for the qth quantile model.

Usage

## S3 method for class 'rq.pen.seq'
qic.select(
  obj,
  method = c("BIC", "AIC", "PBIC"),
  septau = TRUE,
  tauWeights = NULL,
  ...
)

Arguments

obj	A rq.pen.seq or rq.pen.seq.cv object.
method	Choice of BIC, AIC or PBIC, a large p BIC.
septau	If optimal values of \lambda and a can vary with \tau. Default is TRUE.
tauWeights	Weights for each quantile. Useful if you set septau to FALSE but want different weights for the different quantiles. If not specified default is to have w_q=1 for all quantiles.
...	Additional arguments.

Value

• coefficientsCoefficients of the selected models.

• icInformation criterion values for all considered models.

• modelsInfoModel info for the selected models related to the original object obj.

• gicInformation criterion summarized across all quantiles. Only returned if septau set to FALSE

Author(s)

Ben Sherwood, [e-mail]

References

\insertRef

qrbicrqPen

Examples

set.seed(1)
x <- matrix(runif(800),ncol=8)
y <- 1 + x[,1] + x[,8] + (1+.5*x[,3])*rnorm(100)
m1 <- rq.pen(x,y,penalty="ENet",a=c(0,.5,1),tau=c(.25,.75))
qic.select(m1)

rqPen documentation built on Aug. 25, 2023, 1:07 a.m.