qic.select: 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 m_i \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

qic.select(obj, ...)

Arguments

obj	A rq.pen.seq or rq.pen.seq.cv object.
...	Additional arguments see qic.select.rq.pen.seq() or qic.select.rq.pen.seq.cv() for more information.

Value

Returns a qic.select object.

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 April 12, 2025, 1:55 a.m.