rqPen (version 4.1.3)

qic.select: 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 $$\log (\sum _{i=1}^n{w}_i{\rho }_{\tau }(y_i-x_i^{\mathrm{\top }}\hat{\beta }))+d\ast b/(2n),$$ 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 $d=log(n)\ast log(p)$ 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 $$\sum _{q=1}^Q{w}_q[\log (\sum _{i=1}^n{m}_i{\rho }_{\tau }(y_i-x_i^{\mathrm{\top }}{\hat{\beta }}^q))+d_q\ast b_q/(2n)],$$ where $w_q$ is the weight assigned for the qth quantile model.

Usage

qic.select(obj, ...)

Value

Returns a qic.select object.

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.

Author

Ben Sherwood,

References

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)