scaleTau2(x, c1 = 4.5, c2 = 3.0, consistency = TRUE,
mu.too = FALSE, ...)mu.too=FALSE as by default).mu.too is FALSE as by
default) or two (when mu.too = TRUE) with robust scale or
(location,scale) estimators
$\hat\sigma(x)$ or
$(\hat\mu(x),\hat\sigma(x))$.mad(x,
constant=1) is computed. Robustness weights
$w_i := w_{c1}((x_i - med(X))/ s_0)$ are computed, where
$w_c(u) = max(0, (1 - (u/c)^2)^2)$. The robust location
measure is defined as $\mu(X) := (\sum_i w_i x_i)/(\sum_i w_i)$,
and the robust $\tau (tau)$-estimate is $s(X)^2 :=
s_0^2 * (1/n) \sum_i \rho_{c2}((x_i - \mu(X))/s_0)$,
where $\rho_c(u) = min(c^2, u^2)$.
scaleTau2(*, consistency=FALSE) returns $s(X)$, whereas
this value is divided by its asymptotic limit when consistency =
TRUE as by default. Note that for n = length(x) == 2, all equivariant scale estimates are
proportional, and specifically, scaleTau2(x, consistency=FALSE)
== mad(x, constant=1). See also the reference.
Sn, Qn, mad;
further covOGK for which scaleTau2 was designed.x <- c(1:7, 1000)
sd(x) # non-robust std.deviation
scaleTau2(x)
scaleTau2(x, mu.too = TRUE)Run the code above in your browser using DataLab