genet: Generalized Elastic Net Penalty
In lqa: Penalized Likelihood Inference for GLMs

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

Object of the penalty to handle the Generalized Elastic Net (GENET) penalty (Ulbricht, 2010).

1	genet (lambda = NULL, ...)

`lambda`	three-dimensional tuning parameter. The first component corresponds to the regularization parameter λ. This must be a nonnegative real number. The second component 0 ≤q α ≤q 1 drives the linear combination of L_1 penalty and the bridge penalty. The third component indicates the exponent γ of the bridge penalty term. See details below. It must hold that γ > 1.
`...`	further arguments.

The GENET penalty can be defined as

P_{\bar{λ}}^{genet}(\boldsymbol{β}) = λ ≤ft\{α ∑_{i=1}^p |β_i| + (1-α) ∑_{i=1}^p |β_i|^γ \right\}, \quad 0 ≤q α ≤q 1, \: γ > 1

with tuning parameter vector \bar{λ} = (λ, α, γ).

The regularization parameter λ determines the overall relevance of the GENET penalty. The balance between L_1-norm penalization, and hence variable selection, and bridge penalization for incorporating the grouping effect is managed by an overall tuning parameter α. For motivation and further details on the GENET penalty see Ulbricht (2010).

An object of the class penalty. This is a list with elements