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#************************************************************************
#** nl.mscale function **
#** # Scale M-estimator with 50% breakdown **
#** # Yohai (1987) Annals, Stromberg (1993) JASA. **
#** # **
#** # GKS 2 June 99 **
#** # **
#** use newton raphson to solve **
#** (1/n) sum(rho(ri/sgm)) = b **
#** by modified itterated weighted least square. **
#** sgm(n+1) = sgm * [ 1 + d1/d2 ] **
#** d1 = 1/n sum(rho(ri/sgm*k1)) **
#** d2 = 1/n sum( ri/k.sgm psi(ri/ksgm) ) **
#** **
#** Re aranged by Hossein Riazoshams. **
#** 23/09/2009 **
#************************************************************************
nl.mscale <- function(u,robfunc,...)
{
if(mean(u == 0) >= 0.5) return(0)
U <- abs(u)
s <- median(U)/0.6744898
iter <- 0
repeat {
iter <- iter + 1
z <- u/robfunc$arguments$k0/s
rhof <- robfunc$fnc(z,...)
d1 <- mean(as.numeric(rhof)) - robfunc$arguments$maxrho5
d2 <- mean(z * attr(rhof,"gradient"))
s <- s * (1 + d1/d2)
if(iter > 50) {
return(Fault(FN=1,FF="nl.mscale"))
}
if(abs(d1/d2) < 1e-014)
break
}
return(s)
}
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