tukeyChi {robustbase} | R Documentation |
Computes Tukey's bi-square loss function, chi(x)
and its
first two derivatives. Note that in the general context of
M-estimators, these loss functions are called
rho-functions.
tukeyChi(x, cc, deriv = 0)
x |
numeric vector. |
cc |
tuning constant |
deriv |
integer in \{0,1,2\} specifying the order of the
derivative; the default, |
a numeric vector of the same length as x
.
tukeyChi(x, d)
and tukeyPsi1(x, d-1)
are just
re-scaled versions of each other (for d in 0:2
).
Matias Salibian-Barrera and Martin Maechler
op <- par(mfrow = c(3,1), oma = c(0,0, 2, 0), mgp = c(1.5, 0.6, 0), mar= .1+c(3,4,3,2)) x <- seq(-2.5, 2.5, length = 201) cc <- 1.55 # as set by default in lmrob.control() plot. <- function(...) { plot(...); abline(h=0,v=0, col="gray", lty=3)} plot.(x, tukeyChi(x, cc), type = "l", col = 2) plot.(x, tukeyChi(x, cc, deriv = 1), type = "l", col = 2) plot.(x, tukeyChi(x, cc, deriv = 2), type = "l", col = 2) mtext(sprintf("tukeyChi(x, c = %g, deriv), deriv = 0,1,2", cc), outer = TRUE, font = par("font.main"), cex = par("cex.main")) par(op)