# Huber: Multivariate Huber's M-estimator and its symmetrized version In SpatialNP: Multivariate Nonparametric Methods Based on Spatial Signs and Ranks

## Description

Iterative algorithms to estimate M-estimators of location and scatter as well as symmetrized M-estimator using Huber's weight functions.

## Usage

 ```1 2 3 4 5``` ```mvhuberM(X, qg = 0.9, fixed.loc = FALSE, location = NULL, init = NULL, steps = Inf, eps = 1e-06, maxiter = 100, na.action = na.fail) symmhuber(X, qg = 0.9, init = NULL, steps = Inf, eps = 1e-6, maxiter = 100, na.action = na.fail) ```

## Arguments

 `X` a matrix or a data frame `qg` a tuning parameter. The default is 0.9, see details `fixed.loc` a logical, see details `location` an optional vector giving the location of the data or the initial value for the location if it is estimated `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) `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

`mvhuberM` computes multivariate M-estimators of location and scatter using Huber's weight functions. The tuning parameter `qg` defines cutoff-point c for weight functions so that c=F^{-1}(q), where F is the cdf of chi^2-distribution with p degrees of freedom. The estimators with maximal breakdown point are obtained with the choice qg=F(p+1). If `fixed.loc` is set TRUE, scatter estimator is computed with fixed location given by `location` (default is column means).

`symmhuber` computes Huber's M-estimator of scatter using pairwise differences of the data therefore avoiding location estimation.

## Value

`mvhuberM` returns a list with components

 `location ` a vector `scatter ` a matrix

`symmhuber` returns a matrix.

## Author(s)

Klaus Nordhausen, [email protected],
Jari Miettinen, [email protected]

## References

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

Lopuhaa, H.P. (1989). On the relation between S-estimators and M-estimators of multivariate location and covariance. Annals of Statistics, 17, 1662-1683.

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

## Examples

 ```1 2 3 4``` ```A<-matrix(c(1,2,-3,4,3,-2,-1,0,4),ncol=3) X<-matrix(rnorm(1500),ncol=3)%*%t(A) mvhuberM(X) symmhuber(X) ```

SpatialNP documentation built on Sept. 12, 2017, 5:02 p.m.