scaleTau2 {robustbase}R Documentation

Robust Tau-Estimate of Scale

Description

Computes the robust tau-estimate of univariate scale, as proposed by Maronna and Zamar (2002); improved by a consistency factor.

Usage

scaleTau2(x, c1 = 4.5, c2 = 3.0, consistency = TRUE,
          mu.too = FALSE, ...)

Arguments

x numeric vector
c1,c2 non-negative numbers, specifying cutoff values for the biweighting of the mean and the rho function respectively.
mu.too logical indicating if both location and scale should be returned or just the scale (when mu.too=FALSE as by default).
consistency logical indicating if the consistency correction factor (for the scale) should be applied.
... potentially additional arguments which are not used.

Details

First, s0 := MAD, i.e. the equivalent of 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 μ(X) := (sum_i w_i x_i)/(sum_i w_i), and the robust tau-estimate is s(X)^2 := s_0^2 * (1/n) sum_i rho_{c2}((x_i - μ(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.

Value

numeric vector of length one (if mu.too is FALSE as by default) or two (when mu.too = TRUE) with robust scale or (location,scale) estimators s^(x) or (m^(x), s^(x)).

Author(s)

Original by Kjell Konis with substantial modifications by Martin Maechler.

References

Maronna, R.A. and Zamar, R.H. (2002) Robust estimates of location and dispersion of high-dimensional datasets; Technometrics 44(4), 307–317.

See Also

Sn, Qn, mad; further covOGK for which scaleTau2 was designed.

Examples

x <- c(1:7, 1000)
sd(x) # non-robust std.deviation
scaleTau2(x)
scaleTau2(x, mu.too = TRUE)

[Package robustbase version 0.4-5 Index]