hr05CriticalValue {CerioliOutlierDetection}R Documentation

Hardin and Rocke (2005) Critical Value for Testing MCD-based Mahalanobis Distances


Hardin and Rocke (2005) provide an approximate F distribution for testing whether Mahalanobis distances calculated using the MCD dispersion estimate are unusually large, and hence, indicative of outliers in the data.


hr05CriticalValue(em, p.dim, signif.alpha)



(Numeric) Degrees of freedom for Wishart distribution approximation to the MCD scatter matrix.


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


(Numeric) Significance level for testing the null hypothesis


Hardin and Rocke (2005) derived an F distributional approximation for the Mahalanobis distances of the observations that were excluded from the MCD calculation; see equation 3.2 on page 938 of the paper.

It is assumed here that the MCD covariance estimate used in the Mahalanobis distance calculation was adjusted by the consistency factor, so it is not included in the calculation here. (If one needs the consistency factor it is returned by the function ch99AsymptoticDF in this package or by the function .MCDcons in the robustbase package.)


The appropriate cutoff value (from the F distributional approximation) for testing whether a Mahalanobis distance is unusually large at the specified significance level.


It can happen that one of the F distribution paramaters, m - p + 1, is non-positive, in which case qf will return NaN. hr05CriticalValue will issue a warning in this case, and return NA.


Written and maintained by Christopher G. Green <>


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

See Also

hr05AdjustedDF, hr05CutoffMvnormal


hr05CriticalValue( hr05AdjustedDF( 1000, 20 ), 20, 0.05 ) 

[Package CerioliOutlierDetection version 1.1.9 Index]