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, ...)
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.