SpatialNP (version 1.1-5)

symm.mvtmle: 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)

Value

symm.mvtmle returns a matrix.

symm.mvtmle.inc returns a matrix.

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.

Author

Jari Miettinen, ,
Klaus Nordhausen,

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.

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)