weight.funs {robust}

Weight Functions Psi, Rho, Chi

Description

These functions compute the weights used by lmRob and its associated methods.

Usage

psi.weight(x, ips = 1, xk = 1.06)
rho.weight(x, ips = 1, xk = 1.06)
psp.weight(x, ips = 1, xk = 1.06)
chi.weight(x, ips = 1, xk = 1.06)

Arguments

x

a numeric vector.

ips

integer determining the weight function:

ips = 1

"optimal"

,

ips = 2

rescaled bisquare

,

ips = 3

Huber

,

ips = 4

smoothed Huber

, which is currently only available for psi.*() and its derivative psp.*().

xk

a numeric value specifying the tuning constant.

Details

See the section “Theoretical Details”, p. 58-59, in chapter 2 of ‘Robust.pdf’.

Value

a numeric vector, say r of the same length as x, containing the function values r_i = f(x_i).

Examples

x <- seq(-4,4, length=401)
f.x <- cbind(psi = psi.weight(x), psp = psp.weight(x),
             chi = chi.weight(x), rho = rho.weight(x))
es <- expression(psi(x), {psi*minute}(x), chi(x), rho(x))
leg <- as.expression(lapply(seq_along(es), function(i)
          substitute(C == E, list(C=colnames(f.x)[i], E=es[[i]]))))
matplot(x, f.x, type = "l", lwd = 1.5,
        main = "psi.weight(.) etc -- 'optimal'")
abline(h = 0, v = 0, lwd = 2, col = "#D3D3D380") # opaque gray
legend("bottom", leg, inset = .01,
       lty = 1:4, col = 1:4, lwd = 1.5, bg = "#FFFFFFC0")