robLoc | R Documentation |
Compute the robust estimate of location for very small samples.
robLoc(x, scale = NULL, na.rm = FALSE, maxit = 80L, tol = sqrt(.Machine$double.eps))
x |
A numeric vector. |
scale |
The scale, if known, can be used to enhance the estimate for the location; defaults to unknown. |
na.rm |
If |
maxit |
The maximum number of iterations; defaults to 80. |
tol |
The desired accuracy. |
Computes the M-estimator for location using the logistic ψ function of
Rousseeuw & Verboven (2002, 4.1). If there are three or fewer entries, the
function defaults to the median
.
If the scale is known and passed through scale
, the algorithm uses the
suggestion in Rousseeuw & Verboven section 5 (2002), substituting the known
scale for the mad
.
If na.rm
is TRUE
then NA
values are stripped from x
before computation takes place. If this is not done then an NA
value in
x
will cause mad
to return NA
.
The tolerance and number of iterations are similar to those in existing base R functions.
Rousseeuw & Verboven suggest using this function when there are 3–8 samples. It is implied that having more than 8 samples allows the use of more standard estimators.
Solves for the robust estimate of location, Tn, which is the solution to
mean(ψ((xi - Tn)/Sn)) = 0
where Sn is fixed at mad(x)
. The ψ-function selected
by Rousseeuw & Verboven is:
ψ(x) = (exp(x) - 1) / (exp(x) + 1)
This is equivalent to 2 * plogis(x) - 1
.
Avraham Adler Avraham.Adler@gmail.com
Rousseeuw, Peter J. and Verboven, Sabine (2002) Robust estimation in very small samples. Computational Statistics & Data Analysis, 40, (4), 741–758. doi: 10.1016/S0167-9473(02)00078-6
median
robLoc(c(1:9)) x <- c(1,2,3,5,7,8) robLoc(x)
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