get.Amat: Computation of the approximated penalty matrix.

Description

The function get.Amat computes and returns $$\mathbf{A}_\lambda = \sum_{j=1}^J \frac{p_{\lambda,j}'(|\mathbf{a}_j^\top \boldsymbol{\beta}|)}{\sqrt{(\mathbf{a}_j^\top \boldsymbol{\beta})^2 + c}}\mathbf{a}_j\mathbf{a}_j^\top,$$ where $c > 0$ is a small real number. However, this function is primarily intended for internal use. It acts as a link between penalty objects and methods which require the approximated penalty matrix $\mathbf{A}_\lambda$.

Usage

get.Amat (initial.beta = NULL, penalty = NULL, intercept = TRUE, 
     c1 = lqa.control()$c1, x = NULL, ...)

Arguments

initial.beta

the current beta vector.

penalty

member of the penalty class, the penalty to be used.

intercept

logical. If `TRUE' an intercept is included in the model.

double: small positive real number used in the approximation of the linear combinations in the penalty.

optional argument containing the original regressor matrix. This will be used by some penalties, such as penalreg or ao.

...

further arguments.

Value

This function returns a $(p \times p)$-dimensional matrix or if an intercept is included a $((p+1) \times (p+1))$-dimensional matrix.

Details

See penalty or the accompanying `User's Guide' for further details on $\mathbf{A}_\lambda$.

Examples

Run this code

penalty <- lasso (lambda = 1.5)
   beta <- c (1, -2, 3, -4)
   get.Amat (initial.beta = beta, penalty = penalty, intercept = FALSE)