hardin_factor_numeric: Compute F distribution factors for approximating the tail of...

In fdaoutlier: Outlier Detection Tools for Functional Data Analysis

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

Description

Computes asymptotically, the factors for F approximation cutoff for (MCD) robust mahalanobis distances according to Hardin and Rocke (2005) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/106186005X77685")}.

Usage

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.

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) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/106186005X77685")} is given by:

c(m-p+1)/(pm) * RMD^2 ~ F_{p, m-p+1}

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}.

Value

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}.

References

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

fdaoutlier documentation built on Oct. 1, 2023, 1:06 a.m.