PLR.CV {LorenzRegression}

Determines the regularization parameter (lambda) in a PLR via cross-validation

Description

PLR.CV undertakes k-fold cross-validation for a Penalized Lorenz Regression. It returns the CV-score associated to each value of the regularization parameter and the index of the optimum.

Usage

PLR.CV(
  formula,
  data,
  penalty = "SCAD",
  h,
  PLR.est = NULL,
  standardize = TRUE,
  weights = NULL,
  eps,
  nfolds = 10,
  foldID = NULL,
  seed.CV = NULL,
  parallel = FALSE,
  ...
)

Arguments

formula

A formula object of the form response ~ other_variables.

data

A data frame containing the variables displayed in the formula.

penalty

penalty used in the Penalized Lorenz Regression. Possible values are "SCAD" (default) or "LASSO".

h

bandwidth of the kernel, determining the smoothness of the approximation of the indicator function.

PLR.est

Output of a call to PLR.wrap corresponding to the estimation of the Penalized Lorenz Regression on the full sample. Default value is NULL in which case the estimation on the full sample is run internally.

standardize

Should the variables be standardized before the estimation process? Default value is TRUE.

weights

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

eps

Step size in the FABS or SCADFABS algorithm. Default value is 0.005.

nfolds

Number of folds. Default value is 10.

foldID

vector taking value from 1 to nfolds specifying the fold index of each observation. Default value is NULL in which case the folds are defined internally.

seed.CV

Should a specific seed be used in the definition of the folds. Default value is NULL in which case no seed is imposed.

parallel

Whether parallel computing should be used to distribute the nfolds computations on different CPUs. Either a logical value determining whether parallel computing is used (TRUE) or not (FALSE, the default value). Or a numerical value determining the number of cores to use.

...

Additional parameters corresponding to arguments passed in Lorenz.SCADFABS or Lorenz.FABS depending on the argument chosen in penalty.

Value

A list with two components

val

vector indicating the CV-score for each value of lambda.

best

index 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

YX_mat <- Data.Incomes[,-2]
PLR <- PLR.wrap(YX_mat, h = nrow(YX_mat)^(-1/5.5), eps=0.01)
PLR.CV(Income ~ ., Data.Incomes, PLR.est = PLR,
       h = nrow(Data.Incomes)^(-1/5.5), eps = 0.01, nfolds = 5)