hr05AdjustedDF | R Documentation |

Computes the degrees of freedom for the adjusted F distribution for testing Mahalanobis distances calculated with the minimum covariance determinant (MCD) robust dispersion estimate (for data with a model normal distribution) as described in Hardin and Rocke (2005) or in Green and Martin (2017).

```
hr05AdjustedDF( n.obs, p.dim, mcd.alpha, m.asy, method = c("HR05", "GM14"))
```

`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. Default value corresponds to the maximum breakdown point case of the MCD. |

`m.asy` |
(Numeric) Asymptotic Wishart degrees of freedom.
The default value uses |

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

Hardin and Rocke (2005) derived an approximate `F`

distribution
for testing robust Mahalanobis distances, computed using the MCD
estimate of dispersion, for outlyingness. This distribution improves
upon the standard `\chi^2`

distribution for identifying outlying
points in data set. The method of Hardin and Rocke was designed to work
for the maximum breakdown point case of the MCD, where

`\alpha = \lfloor (n.obs + p.dim + 1)/2 \rfloor/n.obs.`

Green and Martin (2017) extended
this result to MCD(`\alpha`

), where `\alpha`

controls the
size of the sample used to compute the MCD estimate, as well as the
breakdown point of the estimator.

With argument `method = "HR05"`

the function returns
`m_{pred}`

as given in Equation 3.4 of Hardin and Rocke (2005).
The Hardin and Rocke method is only supported for the maximum breakdown
point case; an error will be generated for other values of `mcd.alpha`

.

The argument `method = "GM14"`

uses the extended methodology
described in Green and Martin (2017) and is available for all values
of `mcd.alpha`

.

Returns the adjusted F degrees of freedom based on the asymptotic value, the dimension of the data, and the sample size.

This function is typically not called directly by users; rather it is used in the construction of other functions.

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")}

`ch99AsymptoticDF`

```
hr05tester <- function(n,p) {
a <- floor( (n+p+1)/2 )/n
hr05AdjustedDF( n, p, a, ch99AsymptoticDF(n,p,a)$m.hat.asy, method="HR05" )
}
# compare to m_pred in table on page 941 of Hardin and Rocke (2005)
hr05tester( 50, 5)
hr05tester( 100,10)
hr05tester( 500,10)
hr05tester(1000,20)
# using default arguments
hr05tester <- function(n,p) {
hr05AdjustedDF( n, p, method="HR05" )
}
# compare to m_pred in table on page 941 of Hardin and Rocke (2005)
hr05tester( 50, 5)
hr05tester( 100,10)
hr05tester( 500,10)
hr05tester(1000,20)
# Green and Martin (2017) improved method
hr05tester <- function(n,p) {
hr05AdjustedDF( n, p, method="GM14" )
}
# compare to m_sim in table on page 941 of Hardin and Rocke (2005)
hr05tester( 50, 5)
hr05tester( 100,10)
hr05tester( 500,10)
hr05tester(1000,20)
```

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