adaptive.lasso: Adaptive Lasso Penalty

Description Usage Arguments Details Value Author(s) References See Also

View source: R/adaptive.lasso.R

Description

Object of the penalty class to handle the adaptive lasso penalty (Zou, 2006).

Usage

1
adaptive.lasso (lambda = NULL, al.weights = NULL, ...)

Arguments

lambda

regularization parameter. This must be a nonnegative real number.

al.weights

weights used for the adaptive lasso penalty.

...

further arguments.

Details

The adaptive lasso penalty (Zou, 2006) is defined as

P_{\tilde{λ}}^{al} (\boldsymbol{β}) = λ ∑_{i=1}^p w_i |β_i|,

where adaptive weights w_i are used for penalizing different coefficients in the L_1-norm penalty. Based on a root-n-consistent estimator \hat{\boldsymbol{β}} of the true parameter vector \boldsymbol{β}, Zou (2006) uses the weight vector \hat\mathbf{w} = (\hat{w}_1,…,\hat{w}_p)^\top with

\hat{w}_j = \frac{1}{|\hatβ_j|^γ}, \quad j = 1, …, p

as estimates for the adaptive weights, where γ > 0 can be chosen arbitrarily. In the n > p case, the MLE can be used for the estimated weights. In the n << p case, a ridge penalized MLE with an optimized regularization parameter might be a good alternative. You can commit any nonnegative weights by using al.weights in the initialization of the corresponding penalty object. If you left it unspecified then al.weights = 1 will be used.

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.

first.derivative

function: This returns the p-dimensional vector of the first derivative of the p penalty terms with respect to |β_i|. However, this function is not really required for adaptive lasso.

Author(s)

Jan Ulbricht

References

Zou, H. (2006) The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101, 1418–1429.

See Also

penalty, lasso


lqa documentation built on May 30, 2017, 3:41 a.m.