TYLERshape {fastM}

Tyler's Shape Matrix

Description

Iterative algorithm to estimate Tyler's shape matrix using a partial Newton-Raphson approach.

Usage

TYLERshape(X, location = TRUE, eps = 1e-06, maxiter = 100)

Arguments

X

numeric data matrix or dataframe. Missing values are not allowed.

location

logical or numeric. If FALSE, it is assumed that the scatter should be computed wrt to the origin. If TRUE the location will be estimated as the mean vector and if it is a numeric vector it will be computed wrt to the given vector.

eps

convergence tolerance, which means that the algorithm stops when the Frobenius norm of the gradient is smaller than eps.

maxiter

maximum number of iterations.

Details

The estimate is based on the new fast algorithm described in Duembgen et al. (2016). Note that Tyler's shape matrix is standardized such that it has determinant 1.

The function does not check if there are observations equal to the mean (if location=TRUE), to the provided location vector or to the origin (if location=FALSE). In these cases the function will fail.

In case maxiter is reached before convergence, the estimate at that iteration is returned and a warning is given.

Value

A list containing:

mu

Estimated location if location=TRUE, otherwise the user specified location.

Sigma

Estimated shape matrix.

iter

Number of iterations of the algorithm.

Author(s)

Lutz Duembgen and Klaus Nordhausen

References

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

Duembgen, L., Nordhausen, K. and Schuhmacher, H. (2016), New algorithms for M-estimation of multivariate location and scatter, Journal of Multivariate Analysis, 144, 200–217. doi: 10.1016/j.jmva.2015.11.009

See Also

tyler.shape

Examples

TYLERshape(longley)
# compare to
# library(ICSNP)
# tyler.shape(longley)

TYLERshape(longley, location=FALSE)
# compare to
# library(ICSNP)
# tyler.shape(longley, location=0)