| 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)