R: Safe (generalized) Huber M-Estimator of Location

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),
           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.

### 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 τ correction factor but no finite sample correction.

### 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, 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))

[Package robustbase version 0.93-9 Index]