Safe (generalized) Huber M-Estimator of Location
(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),
se = FALSE,
warn0scale = getOption("verbose"))x |
numeric vector. |
k |
positive factor; the algorithm winsorizes at |
weights |
numeric vector of non-negative weights of same length
as |
tol |
convergence tolerance. |
mu |
initial location estimator. |
s |
scale estimator held constant through the iterations. |
se |
logical indicating if the standard error should be computed
and returned (as |
warn0scale |
logical; if true, and |
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.
When se = TRUE, the standard error is computed using the
τ correction factor but no finite sample correction.
list of location and scale parameters, and number of iterations used.
mu |
location estimate |
s |
the |
it |
the number of “Huber iterations” used. |
Martin Maechler, building on the MASS code mentioned.
Huber, P. J. (1981) Robust Statistics. Wiley.
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, se=TRUE), digits = 7) ## should be ~= Hx
stopifnot(all.equal(Hx[-4], Hx.[-4]))
str(Hx2 <- huberM(x, se=TRUE), digits = 7)## somewhat different, since 's' differs
## Confirm correctness of std.error :
system.time(
SS <- replicate(10000, vapply(huberM(rnorm(400), se=TRUE), as.double, 1.))
) # ~ 12.2 seconds
rbind(mean(SS["SE",]), sd(SS["mu",]))# both ~ 0.0508
stopifnot(all.equal(mean(SS["SE",]),
sd ( SS["mu",]), tolerance= 0.002))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.