Compute the robust estimate of scale for very small samples.
robScale(x, loc = NULL, implbound = 1e-4, na.rm = FALSE, maxit = 80L,
tol = sqrt(.Machine$double.eps))Solves for the robust estimate of scale, \(S_n\), which is the solution to$$\frac{1}{n}\sum_{i = 1}^n\rho\left(\frac{x_i - T_n}{S_n}\right) = \beta $$
where \(T_n\) is fixed at median(x) and \(\beta\) is fixed at
0.5. The \(\rho\)-function selected by Rousseeuw & Verboven is based on the
square of the \(\psi\)-function used in robLoc. Specifically
$$\rho_{log}(x) = \psi_{log}^2\left(\frac{x}{0.37394112142347236}\right)
$$
The constant 0.37394112142347236 is necessary so that $$\beta = \int\rho(u)\;d\Phi(u)=0.5$$
A numeric vector.
The location, if known, can be used to enhance the estimate for the scale; defaults to unknown.
The smallest value that mad is allowed before being
considered too close to 0.
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 scale using a smooth \(\rho\)-function defined as
the square of the logistic \(\psi\) function used in location estimation
(Rousseeuw & Verboven, 2002, 4.2). When the sequence of observations is too
short for a robust estimate, the scale estimate will default to mad so
long as mad has not “imploded”, i.e. it is greater than
implbound which defaults to 0.0001. When mad has imploded,
adm is used instead.
If the location is known and passed through loc, the algorithm uses the
suggestion in Rousseeuw & Verboven section 5 (2002) converting the observations
to distances from 0 and iterating on the adjusted sequence.
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")
adm and mad as basic robust estimators of scale.
Qn and Sn in the
robustbase package
which are specialized robust scale estimators for larger samples. The latter two
are based on code written by Peter Rousseeuw.
robScale(c(1:9))
x <- c(1,2,3,5,7,8)
c(robScale(x), robScale(x, loc = 5))
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