tyler.shape: Tyler's Shape Matrix

In ICSNP: Tools for Multivariate Nonparametrics

Tyler's Shape Matrix

Description

Iterative algorithm to estimate Tyler's shape matrix.

Usage

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

Arguments

X	numeric data matrix or dataframe.
location	if NULL the sample mean is used, otherwise a vector with the location can be specified.
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
print.it	logical. If TRUE prints the number of iterations, otherwise not.
na.action	a function which indicates what should happen when the data contain 'NA's. Default is to fail.

Details

The most robust M-estimator of shape. It is proportional to the regular covariance matrix for elliptical contoured distributions. The estimate is in such a way standardized, that its determinate is 1.

The algorithm requires an estimate of location, if none is provided, the sample mean is used. Observations which are equal to the location estimate are removed form the data.

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.

A different implementation is available in the package fastM as the function TYLERshape.

Value

A matrix.

Author(s)

Klaus Nordhausen, and Seija Sirkia

References

Tyler, D.E. (1987), A distribution-free M-estimator of scatter, Annals of Statistics, 15, 234–251.

See Also

duembgen.shape, HR.Mest

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)
tyler.shape(X)
tyler.shape(X, location=0)
cov.matrix/det(cov.matrix)^(1/3)
rm(.Random.seed)

ICSNP documentation built on Sept. 18, 2023, 5:16 p.m.