huberM {robustbase} | R Documentation |
(Generalized) Huber M-estimator of location with MAD scale, being
sensible also when the scale is zero where huber()
returns an error.
huberM(x, k = 1.5, weights = NULL, tol = 1e-06, mu = if(is.null(weights)) median(x) else wgt.himedian(x, weights), s = if(is.null(weights)) mad(x, center=mu) else wgt.himedian(abs(x - mu), weights), warn0scale = getOption("verbose"))
x |
numeric vector. |
k |
positive factor; the algorithm winsorizes at k
standard deviations. |
weights |
numeric vector of non-negative weights of same length
as x , or NULL . |
tol |
convergence tolerance. |
mu |
initial location estimator. |
s |
scale estimator held constant through the iterations. |
warn0scale |
logical; if true, and s is 0 and
length(x) > 1 , this will be warned about. |
Note that currently, when non-NULL
weights
are
specified, the default for initial location mu
and scale
s
is wgt.himedian
, where strictly speaking a
weighted “non-hi” median should be used for consistency.
Since s
is not updated, the results slightly differ, see the
examples below.
list of location and scale parameters, and number of iterations used.
mu |
location estimate |
s |
the s argument, typically the mad . |
it |
the number of “Huber iterations” used. |
Martin Maechler, building on the MASS code mentioned.
Huber, P. J. (1981) Robust Statistics. Wiley.
hubers
(and huber
) in package MASS;
mad
.
huberM(c(1:9, 1000)) mad (c(1:9, 1000)) mad (rep(9, 100)) huberM(rep(9, 100)) ## When you have "binned" aka replicated observations: set.seed(7) x <- c(round(rnorm(1000),1), round(rnorm(50, m=10, sd = 10))) t.x <- table(x) # -> unique values and multiplicities x.uniq <- as.numeric(names(t.x)) ## == sort(unique(x)) x.mult <- unname(t.x) str(Hx <- huberM(x.uniq, weights = x.mult), digits = 7) str(Hx. <- huberM(x, s = Hx$s), digits = 7) ## should be ~= Hx stopifnot(all.equal(Hx, Hx.)) str(Hx2 <- huberM(x), digits = 7)## somewhat different, since 's' differs