robustbase (version 0.5-0-1)

huberM: 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.

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.

concept

robust location

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.

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