# inst/scripts/FiniteSampleCorrectionFactor.R In RobLox: Optimally Robust Influence Curves and Estimators for Location and Scale

```###############################################################################
## Find finite-sample correction factor for asymptotic radius
###############################################################################

library(distr)
library(RobLox)
library(Biobase)

## in combination with sysdata.rda of package RobLox
rowRoblox1 <- function(x, r, k = 1L){
mean <- rowMedians(x, na.rm = TRUE)
sd <- rowMedians(abs(x-mean), na.rm = TRUE)/qnorm(0.75)
if(r > 10){
b <- sd*1.618128043
const <- 1.263094656
A2 <- b^2*(1+r^2)/(1+const)
A1 <- const*A2
a <- -0.6277527697*A2/sd
mse <- A1 + A2
}else{
A1 <- sd^2*RobLox:::.getA1.locsc(r)
A2 <- sd^2*RobLox:::.getA2.locsc(r)
a <- sd*RobLox:::.geta.locsc(r)
b <- sd*RobLox:::.getb.locsc(r)
mse <- A1 + A2
}
robEst <- .kstep.locsc.matrix(x = x, initial.est = cbind(mean, sd),
A1 = A1, A2 = A2, a = a, b = b, k = k)
colnames(robEst\$est) <- c("mean", "sd")
return(robEst\$est)
}

## attaining the maximum finite-sample risk
n <- 10
M <- 1e5
eps <- 0.01
D <- 0.1
fun <- function(r, x, n){
RadMinmax <- rowRoblox1(x, r = r)
}

r <- rbinom(n*M, prob = eps, size = 1)
Mid <- rnorm(n*M)
Mcont <- rep(D, n*M)
Mre <- matrix((1-r)*Mid + r*Mcont, ncol = n)
ind <- rowSums(matrix(r, ncol = n)) >= n/2
while(any(ind)){
M1 <- sum(ind)
cat("M1:\t", M1, "\n")
r <- rbinom(n*M1, prob = eps, size = 1)
Mid <- rnorm(n*M1)
Mcont <- r(contD)(n*M1)
Mre[ind,] <- (1-r)*Mid + r*Mcont
ind[ind] <- rowSums(matrix(r, ncol = n)) >= n/2
}

fun(r = 1, x = Mre, n = n)

fun1 <- function(D){
Mcont <- rep(D, n*M)
Mre <- matrix((1-r)*Mid + r*Mcont, ncol = n)
fun(r = 1, x = Mre, n = n)
}
sapply(c(seq(0.1, 10, length = 20), 20, 50, 100, 1000, 1e4, 1e6), fun1)

## n at least 3, for n = 2 not possible to have less than 50% contamination
n <- c(3:50, seq(55, 100, by = 5), seq(110, 200, by = 10), seq(250, 500, by = 50))
eps <- c(seq(0.001, 0.01, by = 0.001), seq(0.02, to = 0.5, by = 0.01))
M <- 1e5
contD <- Dirac(1e6)

r.fi <- matrix(NA, nrow = length(eps), ncol = length(n))
colnames(r.fi) <- n
rownames(r.fi) <- eps
r.as <- r.fi
for(j in seq(along = n)){
ptm <- proc.time()
cat("aktuelles n:\t", n[j], "\n")
i <- 0
repeat{
i <- i + 1
cat("aktuelles eps:\t", eps[i], "\n")
r <- rbinom(n[j]*M, prob = eps[i], size = 1)
Mid <- rnorm(n[j]*M)
Mcont <- r(contD)(n[j]*M)
Mre <- matrix((1-r)*Mid + r*Mcont, ncol = n[j])
rm(Mid, Mcont)
gc()
ind <- rowSums(matrix(r, ncol = n[j])) >= n[j]/2
rm(r)
gc()
while(any(ind)){
M1 <- sum(ind)
cat("M1:\t", M1, "\n")
r <- rbinom(n[j]*M1, prob = eps[i], size = 1)
Mid <- rnorm(n[j]*M1)
Mcont <- r(contD)(n[j]*M1)
Mre[ind,] <- (1-r)*Mid + r*Mcont
ind[ind] <- rowSums(matrix(r, ncol = n[j])) >= n[j]/2
rm(Mid, Mcont, r)
gc()
}
fun <- function(r, x, n){
RadMinmax <- rowRoblox1(x, r = r)
}
r.fi[i,j] <- optimize(fun, interval = c(eps[i], min(max(2, n[j]*eps[i]*25), 10)), x = Mre, n = n[j])\$minimum
r.as[i,j] <- sqrt(n[j])*eps[i]
cat("finit:\t", r.fi[i,j], "\t asympt:\t", r.as[i,j], "\n")
rm(Mre)
gc()
if(round(r.fi[i,j], 2) == 1.74 | i == length(eps)) break
}
save.image(file = "FiniteSample1.RData")
cat("Dauer:\t", proc.time() - ptm, "\n")
}

r.as <- outer(eps, sqrt(n))
r.fi[is.na(r.fi)] <- 1.74
r.finite <- round(pmax(r.fi, r.as, na.rm = TRUE), 4)

finiteSampleCorrection <- function(r, n){
if(r >= 1.74) return(r)

eps <- r/sqrt(n)
ns <- c(3:50, seq(55, 100, by = 5), seq(110, 200, by = 10),
seq(250, 500, by = 50))
epss <- c(seq(0.001, 0.01, by = 0.001), seq(0.02, to = 0.5, by = 0.01))
if(n %in% ns){
ind <- ns == n
}else{
ind <- which.min(abs(ns-n))
}
return(approx(x = epss, y = finiteSampleRadius[,ind], xout = eps, rule = 2)\$y)
}
```

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RobLox documentation built on April 6, 2019, 3:04 a.m.