hardin_factor_numeric function

Compute F distribution factors for approximating the tail of the distribution of robust MCD distance.

Computes asymptotically, the factors for F approximation cutoff for (MCD) robust mahalanobis distances according to Hardin and Rocke (2005) tools:::Rd_expr_doi("10.1198/106186005X77685") .

hardin_factor_numeric(n, dimension)

Arguments

• n: A numeric value indicating the number of observations of the data.
• dimension: A numeric value indicating the number of variables of the data.

Returns

Returns a list containing: - factor1: then estimated value of $c(m-p+1)/(pm)$ based on n and dimension. - factor2: the value of $F_{p, m-p+1}$.

Details

This function computes the two factors needed for the determining an appropriate cutoff for robust mahalanobis distances computed using the MCD method.

The F approximation according to Hardin and Rocke (2005) tools:::Rd_expr_doi("10.1198/106186005X77685")

is given by:

where $m$ is a parameter for finding the degree of freedom of the $F$ distribution, $c$ is a scaling constant and $p$ is the dimension. The first factor returned by this function (factor1) is $c(m-p+1)/(pm)$ and the second factor (factor2) is $F_{p, m-p+1}$.

References

Hardin, J., and Rocke, D. M. (2005). The distribution of robust distances. Journal of Computational and Graphical Statistics, 14(4), 928-946.