hr05CriticalValue | R Documentation |

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)
```

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

`p.dim` |
(Integer) Dimension of the data, i.e., number of variables. |

`signif.alpha` |
(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 <christopher.g.green@gmail.com>

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")}

`hr05AdjustedDF`

, `hr05CutoffMvnormal`

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

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