This package implements the computation of the bounds described in the article Derumigny, Girard, and Guyonvarch (2021), Explicit non-asymptotic bounds for the distance to the first-order Edgeworth expansion, arxiv:2101.05780.
You can install the release version from the CRAN:
install.packages("BoundEdgeworth")
or the development version from GitHub:
# install.packages("remotes")
remotes::install_github("AlexisDerumigny/BoundEdgeworth")
Let
The goal of this package is to compute values of
or of the form
are valid. Here
The first type of bounds is returned by the function Bound_BE()
(Berry-Esseen-type bound) and the second type (Edgeworth expansion-type
bound) is returned by the function Bound_EE1()
.
Note that these bounds depends on the assumptions made on
- the variables
$X_1, \dots, X_n$ are identically distributed, - the skewness (normalized third moment) of
$X_1, \dots, X_n$ are all$0$ , respectively. - the distribution of
$X_1, \dots, X_n$ admits a continuous component.
setup = list(continuity = FALSE, iid = TRUE, no_skewness = FALSE)
Bound_EE1(setup = setup, n = 1000, K4 = 9)
#> [1] 0.1626857
This shows that
as soon as the variables
Adding one more regularity assumption on the distribution of the
setup = list(continuity = TRUE, iid = TRUE, no_skewness = FALSE)
Bound_EE1(setup = setup, n = 1000, K4 = 9, regularity = list(kappa = 0.99))
#> [1] 0.1214038
This shows that
in this case.