Compute the robust estimate of location for very small samples.
robLoc(x, scale = NULL, na.rm = FALSE, maxit = 80L, tol = sqrt(.Machine$double.eps))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.
A numeric vector.
The scale, if known, can be used to enhance the estimate for the location; defaults to unknown.
If TRUE then NA values are stripped from x
before computation takes place.
The maximum number of iterations; defaults to 80.
The desired accuracy.
Avraham Adler Avraham.Adler@gmail.com
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.
Rousseeuw, Peter J. and Verboven, Sabine (2002) Robust estimation in very small samples. Computational Statistics & Data Analysis, 40, (4), 741--758. tools:::Rd_expr_doi("10.1016/S0167-9473(02)00078-6")
robLoc(c(1:9))
x <- c(1,2,3,5,7,8)
robLoc(x)
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