robLoc {revss} | R Documentation |
Robust Estimate of Location
Description
Compute the robust estimate of location for very small samples.
Usage
robLoc(x, scale = NULL, na.rm = FALSE, maxit = 80L, tol = sqrt(.Machine$double.eps))
Arguments
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. |
Details
Computes the M-estimator for location using the logistic \psi
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.
Value
Solves for the robust estimate of location, T_n
, which is the solution
to
\frac{1}{n}\sum_{i = 1}^n\psi\left(\frac{x_i - T_n}{S_n}\right) = 0
where S_n
is fixed at mad(x)
. The \psi
-function selected
by Rousseeuw & Verboven is:
\psi_{log}(x) = \frac{e^x - 1}{e^x + 1}
This is equivalent to 2 * plogis(x) - 1
.
Author(s)
Avraham Adler Avraham.Adler@gmail.com
References
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
See Also
Examples
robLoc(c(1:9))
x <- c(1,2,3,5,7,8)
robLoc(x)