Lorenz.boot {LorenzRegression} | R Documentation |
Bootstrap for the (penalized) Lorenz regression
Description
Lorenz.boot
performs bootstrap estimation for the vector of coefficients of the single-index model, the explained Gini coefficient, and the Lorenz-R^2
. In the penalized case, it also provides a selection method.
Usage
Lorenz.boot(
object,
R,
boot_out_only = FALSE,
store_LC = FALSE,
show_progress = TRUE,
...
)
Arguments
object |
An object of class |
R |
An integer specifying the number of bootstrap replicates. |
boot_out_only |
A logical value indicating whether the function should return only the raw bootstrap output. This advanced feature can help save computation time in specific use cases. See Details. |
store_LC |
A logical determining whether explained Lorenz curves ordinates should be stored for each bootstrap sample. The default is |
show_progress |
A logical. If |
... |
Additional arguments passed to either the bootstrap function |
Details
The function supports parallel computing in two ways:
Using the built-in parallelization options of
boot
, which can be controlled via the...
arguments such asparallel
,ncpus
, andcl
.Running multiple independent instances of
Lorenz.boot()
, each handling a subset of the bootstrap samples. In this case, settingboot_out_only = TRUE
ensures that the function only returns the raw bootstrap results. These results can be merged usingLorenz.boot.combine
.
Handling of additional arguments (...
):
The function allows for two types of arguments through ...
:
Arguments for
boot
, used to control the bootstrap procedure.Arguments for the underlying fit functions (
Lorenz.GA
,Lorenz.FABS
, orLorenz.SCADFABS
). By default, the function retrieves these parameters from the originalLorenz.Reg
call. However, users can override them by explicitly specifying new values in...
.
Value
An object of class c("LR_boot", "LR")
or c("PLR_boot", "PLR")
, depending on whether a non-penalized or penalized regression was fitted.
The methods confint.LR
and confint.PLR
can be used on objects of class "LR_boot"
or "PLR_boot"
to construct confidence intervals for the model parameters.
For the non-penalized Lorenz regression, the returned object is a list containing:
theta
The estimated vector of parameters. In the penalized case, this is a matrix where each row corresponds to a different selection method (e.g., BIC, bootstrap, cross-validation).
Gi.expl
The estimated explained Gini coefficient. In the penalized case, this is a vector, where each element corresponds to a different selection method.
LR2
The Lorenz-
R^2
of the regression. In the penalized case, this is a vector, where each element corresponds to a different selection method.boot_out
An object of class
"boot"
containing the raw bootstrap output.
For the penalized Lorenz regression, the returned object includes:
path
See
Lorenz.Reg
for the original path. The out-of-bag (OOB) score is added.lambda.idx
A vector indicating the index of the optimal lambda obtained by each selection method.
grid.idx
A vector indicating the index of the optimal grid parameter obtained by each selection method.
Note: In the penalized case, the returned object may have additional classes such as "PLR_cv"
if cross-validation was performed and used for selection.
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 (2024). A penalized bootstrap estimation procedure for the explained Gini coefficient. Electronic Journal of Statistics 18(1) 247-300.
See Also
Lorenz.Reg
, Lorenz.GA
, Lorenz.SCADFABS
, Lorenz.FABS
, PLR.CV
, boot
Examples
# Non-penalized regression example (not run due to execution time)
## Not run:
set.seed(123)
NPLR_boot <- Lorenz.boot(NPLR, R = 30)
confint(NPLR_boot) # Confidence intervals
summary(NPLR_boot)
## End(Not run)
# Penalized regression example:
set.seed(123)
PLR_boot <- Lorenz.boot(PLR, R = 20)
print(PLR_boot)
summary(PLR_boot)
coef(PLR_boot, pars.idx = "Boot")
predict(PLR_boot, pars.idx = "Boot")
plot(PLR_boot)
plot(PLR_boot, type = "diagnostic")
# Confidence intervals for different selection methods:
confint(PLR_boot, pars.idx = "BIC") # Using BIC-selected tuning parameters
confint(PLR_boot, pars.idx = "Boot") # Using bootstrap-selected tuning parameters