PLR.BIC {LorenzRegression}

Determines the regularization parameter (lambda) in a PLR via optimization of an information criterion.

Description

PLR.BIC takes as input a matrix of estimated parameter vectors, where each row corresponds to a covariate and each column corresponds to a value of lambda, and returns the index of the optimal column by optimizing an information criterion. By default the BIC is used.

Usage

PLR.BIC(YX_mat, theta, weights = NULL, IC = c("BIC", "AIC"))

Arguments

YX_mat

A matrix with the first column corresponding to the response vector, the remaining ones being the explanatory variables.

theta

matrix gathering the path of estimated parameter vectors. Each row corresponds to a given covariate. Each column corresponds to a given value of lambda

weights

vector of sample weights. By default, each observation is given the same weight.

IC

indicates which information criterion is used. Possibles values are "BIC" (default) or "AIC".

Value

A list with two components

val

vector indicating the value attained by the information criterion for each value of lambda.

best

index of the value of lambda where the optimum is attained.

References

Jacquemain, A., C. Heuchenne, and E. Pircalabelu (2022). A penalised bootstrap estimation procedure for the explained Gini coefficient.

See Also

Lorenz.Reg, PLR.wrap, Lorenz.FABS, Lorenz.SCADFABS

Examples

data(Data.Incomes)
YX_mat <- Data.Incomes[,-2]
PLR <- PLR.wrap(YX_mat, h = nrow(YX_mat)^(-1/5.5), eps = 0.005)
PLR.BIC(YX_mat, PLR$theta)