Spatial location {SpatialNP} | R Documentation |
Spatial median, multivariate Hodges-Lehmann estimate of location and their affine equivariant versions
ae.hl.estimate(X, init=NULL, shape=TRUE, maxiter = 500, eps = 1e-6, na.action = na.fail) spatial.location(X, score = c("sign", "signrank"), init = NULL, shape = TRUE, maxiter = 500, eps = 1e-6, na.action = na.fail)
X |
a matrix or a data frame |
score |
a character string indicating which transformation of the observations should be used |
init |
an optional vector giving the initial point of the iteration |
shape |
logical, or a matrix. See details |
eps |
tolerance for convergence |
maxiter |
maximum number of iteration steps |
na.action |
a function which indicates what should happen when the data contain 'NA's. Default is to fail. |
Hodges-Lehmann estimate of multivariate location is the
spatial median (see spatial.median
) of the observations
and their pairwise averages. Since spatial median is not affine
equivariant, neither is multivariate Hodges-Lehmann estimate. Affine
equivariance can be achieved by simultaneously estimating the
corresponding shape, as proposed for the spatial median by
Hettmansperger and Randles (2002). For spatial median the corresponding
shape is tyler.shape
and the simultaneous estimation is
implemented as HR.Mest
, see its documentation for
further details on the algorithm. For the Hodges-Lehmann estimate it
is rank.shape
.
spatial.location
is a wrapper function for a unified access to
both location estimates. The choice of estimate is done via
score
:
"sign"
for spatial median
"signrank"
for Hodges-Lehmann estimate
If a matrix (must be symmetric and positive definite, but this is not
checked) is given as shape
the location estimate is found with
respect to that shape and no further shape estimation is done. If a
logical TRUE
is given as shape
the shape is estimated
and consequently the affine equivariant version of the location
estimate is found. If shape
is FALSE
then shape
estimation is not done and the non affine equivariant version of the
location estimate is found.
The estimate vector with the (final estimate of or given) shape matrix
as attribute "shape"
.
Seija Sirkia, ssirkia@maths.jyu.fi
Hettmansperger, T. and Randles, R. (2002) A Practical Affine Equivariant Multivariate Median, Biometrika, 89, pp. 851-860
spatial.median
, HR.Mest
signrank.shape
A<-matrix(c(1,2,-3,4,3,-2,-1,0,4),ncol=3) X<-matrix(rt(150,1),ncol=3)%*%t(A) spatial.location(X,score="signrank") spatial.location(X,score="sign") #compare with: colMeans(X) ae.hl.estimate(X,shape=A%*%t(A)) ae.hl.estimate(X,shape=FALSE)