Iterative algorithms to estimate M-estimators of location and scatter as well as symmetrized M-estimator using Huber's weight functions.
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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 |
eps |
tolerance for convergence |
maxiter |
maximum number of iteration steps. Ignored if |
na.action |
a function which indicates what should happen when the data contain 'NA's. Default is to fail. |
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.
mvhuberM
returns a list with components
location |
a vector |
scatter |
a matrix |
symmhuber
returns a matrix.
Klaus Nordhausen, klaus.nordhausen@uta.fi,
Jari Miettinen, jari.p.miettinen@jyu.fi
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.
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