| bridge {lqa} | R Documentation |
Bridge Penalty
Description
Object of the penalty to handle the bridge penalty (Frank \& Friedman, 1993, Fu, 1998)
Usage
bridge (lambda = NULL, ...)
Arguments
lambda |
two dimensional tuning parameter parameter. The first component corresponds to the regularization parameter |
... |
further arguments. |
Details
The bridge penalty has been introduced in Frank \& Friedman (1993). See also Fu (1998). It is defined as
P_{\tilde{\lambda}}^{br} (\boldsymbol{\beta}) = \lambda \sum_{i=1}^p |\beta_i|^\gamma, \quad \gamma > 0,
where \tilde{\lambda} = (\lambda, \gamma).
It features an additional tuning parameter \gamma that controls the degree of preference for the
estimated coefficient vector to align with the original, hence standardized, data axis directions in the regressor
space.
It comprises the lasso penalty (\gamma = 1) and the ridge penalty (\gamma = 2) as special cases.
Value
An object of the class penalty. This is a list with elements
penalty |
character: the penalty name. |
lambda |
double: the (nonnegative) regularization parameter. |
getpenmat |
function: computes the diagonal penalty matrix. |
Author(s)
Jan Ulbricht
References
Frank, I. E. \& J. H. Friedman (1993) A statistical view of some chemometrics regression tools (with discussion). Technometrics 35, 109–148.
Fu, W. J. (1998) Penalized Regression: the bridge versus the lasso. Journal of Computational and Graphical Statistics 7, 397–416.
See Also
penalty, lasso, ridge, ao, genet