huberM {robustbase}R Documentation

Safe (generalized) Huber M-Estimator of Location

Description

(Generalized) Huber M-estimator of location with MAD scale, being sensible also when the scale is zero where huber() returns an error.

Usage

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"))

Arguments

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.

Details

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.

Value

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.

Author(s)

Martin Maechler, building on the MASS code mentioned.

References

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

See Also

hubers (and huber) in package MASS; mad.

Examples

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

[Package robustbase version 0.4-3 Index]