| qic.select {rqPen} | R Documentation |
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, ben.sherwood@ku.edu
References
Lee ER, Noh H, Park BU (2014). “Model Selection via Bayesian Information Criterion for Quantile Regression Models.” Journal of the American Statistical Association, 109(505), 216–229. ISSN 01621459.
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)