Lorenz.boot {LorenzRegression}

Produces bootstrap-based inference for (penalized) Lorenz regression

Description

Lorenz.boot determines bootstrap estimators for the weight vector, explained Gini coefficient and Lorenz-R^2 and, if applies, selects the regularization parameter.

Usage

Lorenz.boot(
  formula,
  data,
  standardize = TRUE,
  weights = NULL,
  LR.est = NULL,
  penalty = c("none", "SCAD", "LASSO"),
  h = NULL,
  eps = 0.005,
  B = 500,
  bootID = NULL,
  seed.boot = 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.

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.

LR.est

Estimation on the original sample. Output of a call to Lorenz.GA or PLR.wrap.

penalty

should the regression include a penalty on the coefficients size. If "none" is chosen, a non-penalized Lorenz regression is computed using function Lorenz.GA. If "SCAD" is chosen, a penalized Lorenz regression with SCAD penalty is computed using function Lorenz.SCADFABS. IF "LASSO" is chosen, a penalized Lorenz regression with LASSO penalty is computed using function Lorenz.FABS.

h

Only used if penalty="SCAD" or penalty="LASSO". Bandwidth of the kernel, determining the smoothness of the approximation of the indicator function. Default value is NULL (unpenalized case) but has to be specified if penalty="LASSO" or penalty="SCAD".

eps

Only used if penalty="SCAD" or penalty="LASSO". Step size in the FABS or SCADFABS algorithm. Default value is 0.005.

B

Number of bootstrap resamples. Default is 500.

bootID

matrix where each row provides the ID of the observations selected in each bootstrap resample. Default is NULL, in which case these are defined internally.

seed.boot

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 B 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.GA, Lorenz.SCADFABS or Lorenz.FABS depending on the argument chosen in penalty.

Value

A list with several components:

LR.est

Estimation on the original sample.

Gi.star

In the unpenalized case, a vector gathering the bootstrap estimators of the explained Gini coefficient. In the penalized case, it becomes a list of vectors. Each element of the list corresponds to a different value of the penalization parameter

LR2.star

In the unpenalized case, a vector gathering the bootstrap estimators of the Lorenz-R^2. In the penalized case, it becomes a list of vectors.

theta.star

In the unpenalized case, a matrix gathering the bootstrap estimators of theta (rows correspond to bootstrap iterations and columns refer to the different coefficients). In the penalized case, it becomes a list of matrices.

OOB.total

In the penalized case only. Vector gathering the OOB-score for each lambda value.

OOB.best

In the penalized case only. index of the lambda value attaining the highest OOB-score.

References

Heuchenne, C. and A. Jacquemain (2022). Inference for monotone single-index conditional means: A Lorenz regression approach. Computational Statistics & Data Analysis 167(C). Jacquemain, A., C. Heuchenne, and E. Pircalabelu (2022). A penalised bootstrap estimation procedure for the explained Gini coefficient.

See Also

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

Examples

data(Data.Incomes)
set.seed(123)
Data <- Data.Incomes[sample(1:nrow(Data.Incomes),50),]
Lorenz.boot(Income ~ ., data = Data,
            penalty = "SCAD", h = nrow(Data)^(-1/5.5),
            eps = 0.02, B = 40, seed.boot = 123)