huberM function

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"))

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.

• se: logical indicating if the standard error should be computed and returned (as SE component). Currently only available when weights is NULL.

• warn0scale: logical; if true, and s is 0 and length(x) > 1, this will be warned about.

Returns

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.

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.

When se = TRUE, the standard error is computed using the $\tau$ correction factor but no finite sample correction.

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 list("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, 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.))
) # ~ 2.8 seconds (was 12.2 s)
rbind(mean(SS["SE",]), sd(SS["mu",]))# both ~ 0.0508
stopifnot(all.equal(mean(SS["SE",]),
                    sd ( SS["mu",]), tolerance= 0.002))