CerioliOutlierDetection (version 1.1.15)

hr05CutoffMvnormal: Corrected Critical Values for Testing MCD-based Mahalanobis Distances

Description

Provides critical values for testing for outlyingness using MCD-based Mahalanobis distances and the \(F\) distributional approximation developed by Hardin and Rocke (2005) or the enhancement by Green and Martin (2017).

Usage

hr05CutoffMvnormal(n.obs, p.dim, mcd.alpha, signif.alpha, 
  method = c("GM14", "HR05"), use.consistency.correction = FALSE)

Value

cutoff.pred

Critical value based on the predicted Wishart degrees of freedom m.pred

cutoff.asy

Critical value based on the asymptotic Wishart degrees of freedom m.asy

c.alpha

The value of the consistency correction factor, \(c_{\alpha} \)

m.asy

Asymptotic Wishart degrees of freedom parameter

m.pred

Predicted Wishart degrees of freedom (using the method specified in method)

n.obs

Number of observations

p.dim

Number of variables

Arguments

n.obs

(Integer) Number of observations

p.dim

(Integer) Dimension of the data, i.e., number of variables.

mcd.alpha

(Numeric) Value that determines the fraction of the sample used to compute the MCD estimate. Defaults to the value used in the maximum breakdown point case of the MCD.

signif.alpha

(Numeric) Significance level for testing the null hypothesis. Default value is 0.05.

method

Either "HR05" to use the method of Hardin and Rocke (2005), or "GM14" to use the method of Green and Martin (2017).

use.consistency.correction

(Logical) By default, the method does not multiply the cutoff values by the consistency correction for the MCD, under the assumption that the correction was applied during the calculation of the MCD-based Mahalanobis distances. Specify TRUE to add the correction factor if you need it for your application.

Author

Written and maintained by Christopher G. Green <[e-mail]>

Details

hr05CutoffMvnormal is the typical way in which a user will calculate critical values for testing outlyingness via MCD-based Mahalanobis distances. The critical values come from the \(F\) distributional approximation derived by Hardin and Rocke (2005). One can use either the corrected degrees of freedom parameter derived in that paper (which was only shown to work for the maximum breakdown point case of MCD), or the correction derived in Green and Martin (2017) for arbitrary values of mcd.alpha.

References

C. G. Green and R. Douglas Martin. An extension of a method of Hardin and Rocke, with an application to multivariate outlier detection via the IRMCD method of Cerioli. Working Paper, 2017. Available from https://christopherggreen.github.io/papers/hr05_extension.pdf

J. Hardin and D. M. Rocke. The distribution of robust distances. Journal of Computational and Graphical Statistics, 14:928-946, 2005. tools:::Rd_expr_doi("10.1198/106186005X77685")

See Also

hr05CriticalValue, hr05AdjustedDF

Examples

# examples from page 941 of Hardin and Rocke
hr05CutoffMvnormal(n.obs=50  , p.dim=5 , signif.alpha=0.05)
hr05CutoffMvnormal(n.obs=100 , p.dim=10, signif.alpha=0.05)
hr05CutoffMvnormal(n.obs=500 , p.dim=10, signif.alpha=0.05)
hr05CutoffMvnormal(n.obs=1000, p.dim=20, signif.alpha=0.05)