normal_crit {ICSClust}

Selection of Non-normal Invariant Components Using Marginal Normality Tests

Description

Identifies invariant coordinates that are non normal using univariate normality tests as in the comp.norm.test function from the ICSOutlier package, with the difference that both the first and last few components are investigated.

Usage

normal_crit(object, ...)

## S3 method for class 'ICS'
normal_crit(
  object,
  level = 0.05,
  test = c("agostino.test", "jarque.test", "anscombe.test", "bonett.test",
    "shapiro.test"),
  max_select = NULL,
  select_only = FALSE,
  ...
)

## Default S3 method:
normal_crit(
  object,
  level = 0.05,
  test = c("agostino.test", "jarque.test", "anscombe.test", "bonett.test",
    "shapiro.test"),
  max_select = NULL,
  select_only = FALSE,
  gen_kurtosis = NULL,
  ...
)

Arguments

object

object of class "ICS" or a data frame or matrix.

...

additional arguments are currently ignored.

level

the initial level used to make a decision based on the test p-values. See details. Default is 0.05.

test

name of the normality test to be used. Possibilities are "jarque.test", "anscombe.test", "bonett.test", "agostino.test", "shapiro.test". Default is "agostino.test".

max_select

the maximal number of components to select.

select_only

boolean. If TRUE only the vector names of the selected invariant components is returned. If FALSE additional details are returned.

gen_kurtosis

vector of generalized kurtosis values.

Details

The procedure sequentially tests the first and the last components until finding no additional components as non-normal. The quantile levels are adjusted for multiple testing by taking the level as level/j for the jth component.

Value

If select_only is TRUE a vector of the names of the invariant components or variables to select. If FALSE an object of class "ICS_crit" is returned with the following objects:

• crit: the name of the criterion "normal".

• level: the level of the test.

• max_select: the maximal number of components to select.

• test: name of the normality test to be used.

• pvalues: the p-values of the tests.

• adjusted_levels: the adjusted levels.

• select: the names of the invariant components or variables to select.

• gen_kurtosis: the vector of generalized kurtosis values in case of ICS object.

Author(s)

Andreas Alfons, Aurore Archimbaud, Klaus Nordhausen and Anne Ruiz-Gazen

References

Alfons, A., Archimbaud, A., Nordhausen, K., & Ruiz-Gazen, A. (2022). Tandem clustering with invariant coordinate selection. arXiv preprint arXiv:2212.06108..

Archimbaud, A., Nordhausen, K., and Ruiz-Gazen, A. (2018). ICSOutlier: Unsupervised Outlier Detection for Low-Dimensional Contamination Structure, The RJournal, Vol. 10(1):234–250. doi:10.32614/RJ-2018-034

Archimbaud, A., Nordhausen, K., and Ruiz-Gazen, A. (2016). ICSOutlier: Outlier Detection Using Invariant Coordinate Selection. R package version 0.3-0

See Also

med_crit(), var_crit(), discriminatory_crit(), jarque.test(), anscombe.test(), bonett.test(), agostino.test(), stats::shapiro.test().

Examples

X <- iris[,-5]
out <- ICS(X)
normal_crit(out, level = 0.1, select_only = FALSE)