duembgen.shape {ICSNP}R Documentation

Duembgen's Shape Matrix

Description

Iterative algorithm to estimate Dümbgen's shape matrix.

Usage

duembgen.shape(X, init = NULL, steps = Inf, eps = 1e-06, 
               maxiter = 100, in.R = FALSE, na.action = na.fail, ...)

Arguments

X numeric data matrix or dataframe.
init an optional matrix giving the starting value for the iteration
steps a fixed number of iteration steps to take. See details.
eps convergence tolerance.
maxiter maximum number of iterations.
in.R logical. If TRUE R-code (and not C) is used in the iteration
na.action a function which indicates what should happen when the data contain 'NA's. Default is to fail.
... other arguments passed on to tyler.shape.

Details

Dümbgen's shape matrix can be seen as tyler.shape's matrix wrt to the origin for the pairwise differences of the observations. Therefore this shape matrix needs no location parameter.

The function is, however, slow if the dataset is large.

The algorithm also allows for a k-step version where the iteration is run for a fixed number of steps instead of until convergence. If steps is finite that number of steps is taken and maxiter is ignored.

Value

A matrix.

Author(s)

Klaus Nordhausen, klaus.nordhausen@uta.fi, and Seija Sirkiä, ssirkia@maths.jyu.fi

References

Dümbgen, L. (1998), On Tyler's M-functional of scatter in high dimension, Annals of Institute of Statistical Mathematics, 50, 471–491.

See Also

tyler.shape

Examples

set.seed(654321)
cov.matrix <- matrix(c(3,2,1,2,4,-0.5,1,-0.5,2), ncol=3)
X <- rmvnorm(100, c(0,0,0), cov.matrix)
cov.matrix/det(cov.matrix)^(1/3)
duembgen.shape(X)
rm(.Random.seed)

[Package ICSNP version 1.0-2 Index]