symm.mvtmle: Symmetrized M-estimators of scatter with the weights of the...

In SpatialNP: Multivariate Nonparametric Methods Based on Spatial Signs and Ranks

Symmetrized M-estimators of scatter with the weights of the t-distribution

Description

Iterative algorithms to estimate symmetrized M-estimators of scatter using weights of the t-distribution.

Usage

symm.mvtmle(X, nu=1, init=NULL, steps=Inf, eps=1e-6, 
maxiter=100, na.action = na.fail)

symm.mvtmle.inc(X, nu=1, m=10, init=NULL, steps=Inf, permute=TRUE,
eps=1e-6, maxiter=100, na.action = na.fail)

Arguments

X	a matrix or a data frame
nu	the degrees of freedom of the t-distribution. The default is 1. Must be larger than 0.
init	an optional starting value for scatter
steps	fixed number of iteration steps to take, if Inf iteration is repeated until convergence (or until maxiter steps)
m	a parameter in symm.mvtmle.inc which defines how many pairwise differences are used, see details.
permute	logical in symm.mvtmle.inc which determines whether the rows of X are permuted randomly, see details.
eps	tolerance for convergence
maxiter	maximum number of iteration steps. Ignored if steps is finite
na.action	a function which indicates what should happen when the data contain 'NA's. Default is to fail.

Details

symm.mvtmle computes M-estimator of scatter using weights of the t-distribution and pairwise differences of the data. Hence, location estimation is not needed.

symm.mvtmle.inc is a computationally lighter estimator to approximate symmetrized M-estimator of scatter which uses weights of the t-distribution. Only a subset of the pairwise differences are used in the computation in the incomplete case. The magnitude of the subset used is controlled by the argument m which is half of the number of how many differences each observation is part of. Differences of successive observations are used, and therefore random permutation of the rows of X is suggested and is the default choice in the function. For details see Miettinen et al., 2016.

Value

symm.mvtmle returns a matrix.

symm.mvtmle.inc returns a matrix.

Author(s)

Jari Miettinen, [e-mail],
Klaus Nordhausen, [e-mail]

References

Huber, P.J. (1981), Robust Statistics, Wiley, New York.

Sirkia, S., Taskinen, S., Oja, H. (2007) Symmetrised M-estimators of scatter. Journal of Multivariate Analysis, 98, 1611-1629.

Duembgen, L., Pauly, M., Schweizer, T. (2015) M-Functionals of multivariate scatter. Statistics Surveys 9, 32-105.

Miettinen, J., Nordhausen, K., Taskinen, S., Tyler, D.E. (2016) On the computation of symmetrized M-estimators of scatter. In Agostinelli, C. Basu, A., Filzmoser, P. and Mukherje, D. (editors) ”Recent Advances in Robust Statistics: Theory and Application”, 131-149, Springer India, New Delhi.

Examples

A<-matrix(c(1,2,-3,4,3,-2,-1,0,4),ncol=3)
X<-matrix(rnorm(1500),ncol=3)%*%t(A)
symm.mvtmle(X, nu=2)
symm.mvtmle.inc(X, nu=2, m=20)

SpatialNP documentation built on March 18, 2022, 8:02 p.m.