hr05CutoffMvnormal | R Documentation |
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).
hr05CutoffMvnormal(n.obs, p.dim, mcd.alpha, signif.alpha,
method = c("GM14", "HR05"), use.consistency.correction = FALSE)
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. |
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
.
cutoff.pred |
Critical value based on the predicted
Wishart degrees of freedom |
cutoff.asy |
Critical value based on the asymptotic
Wishart degrees of freedom |
c.alpha |
The value of the consistency correction
factor, |
m.asy |
Asymptotic Wishart degrees of freedom parameter |
m.pred |
Predicted Wishart degrees of freedom
(using the method specified in |
n.obs |
Number of observations |
p.dim |
Number of variables |
Written and maintained by Christopher G. Green <christopher.g.green@gmail.com>
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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/106186005X77685")}
hr05CriticalValue
, hr05AdjustedDF
# 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)
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