penalty_function {GGMncv}

Penalty Function

Description

Compute the penalty function for nonconvex penalties.

Usage

penalty_function(
  theta = seq(-5, 5, length.out = 1e+05),
  penalty = "atan",
  lambda = 1,
  gamma = c(0.01, 0.05)
)

Arguments

theta

Numeric vector. Values for which the derivative is computed.

penalty

Character string. Which penalty should be used (defaults to "atan")? See ggmncv for the available penalties.

lambda

Numeric. Regularization parameter (defaults to 1).

gamma

Numeric vector. Hyperparameter(s) for the penalty function

Value

A list of class penalty_function, including the following:

• deriv: Data frame including the penalty function, theta, gamma, and the chosen penalty.

Note

Some care is required for specifying gamma. For example, the default value for scad is 3.7 and it must be some value greater than 2 (Fan and Li 2001). The default values in GGMncv are set to recommended values in the respective papers.

References

Fan J, Li R (2001). “Variable selection via nonconcave penalized likelihood and its oracle properties.” Journal of the American statistical Association, 96(456), 1348–1360.

Examples

func <- penalty_function(theta =  seq(-5,5,length.out = 10000),
                            lambda = 1,
                            gamma = c(0.01, 0.05, 0.1))

head(func$pen)