# R/getInfRad.R In ROptEst: Optimally Robust Estimation

```###############################################################################
## optimal radius for given clipping bound for asymptotic MSE
###############################################################################

L2deriv = "UnivariateDistribution",
risk = "asMSE",
neighbor = "ContNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
gamm <- getInfGamma(L2deriv = L2deriv, risk = risk, neighbor = neighbor,
biastype = biastype, cent = cent, clip = clip)
return((-gamm/clip)^.5)
})

L2deriv = "UnivariateDistribution",
risk = "asMSE",
neighbor = "TotalVarNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
gamm <- getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype,
cent = if(symm) -clip/2 else cent , clip = clip)
return((-gamm/clip)^.5)
})

L2deriv = "EuclRandVariable",
risk = "asMSE",
neighbor = "UncondNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
Distr, stand, cent, trafo, ...){
gamm <- getInfGamma(L2deriv = L2deriv, risk = risk, neighbor = neighbor,
biastype = biastype, Distr = Distr, stand = stand,
cent = cent, clip = clip, ...)
return((-gamm/clip)^.5)
})

###############################################################################
## optimal radius for given clipping bound for asymptotic L1risk
###############################################################################

L2deriv = "UnivariateDistribution",
risk = "asL1",
neighbor = "ContNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
s <- getInfV(L2deriv, neighbor, biastype, clip, cent, stand=1)
gamm <- getInfGamma(L2deriv = L2deriv, risk = risk, neighbor = neighbor,
biastype = biastype, cent = cent, clip = clip)
solvfct <- function(r){
w <- r * clip / s^.5
dp <- 2*dnorm(w)
pp <- 2*pnorm(w)-1
lhs <- s^.5*r*pp/dp
return(lhs + gamm)
}
r <- try(uniroot(solvfct, lower=1e-5, upper = 10)\$root,silent=TRUE)
if(is(r, "try-error")) return(NA)
return(r)
})

L2deriv = "UnivariateDistribution",
risk = "asL1",
neighbor = "TotalVarNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
s <- getInfV(L2deriv, neighbor, biastype, clip, cent, stand=1)
gamm <- getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype,
cent = if(symm) -clip/2 else cent , clip = clip)
solvfct <- function(r){
w <- r * clip / s^.5
dp <- 2*dnorm(w)
pp <- 2*pnorm(w)-1
lhs <- s^.5*r*pp/dp
return(lhs + gamm)
}
r <- try(uniroot(solvfct, lower=1e-5, upper = 10)\$root,silent=TRUE)
if(is(r, "try-error")) return(NA)
return(r)
})

###############################################################################
## optimal radius for given clipping bound for asymptotic L4 risk
###############################################################################

L2deriv = "UnivariateDistribution",
risk = "asL4",
neighbor = "ContNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
s <- getInfV(L2deriv, neighbor, biastype, clip, cent, stand=1)
gamm <- getInfGamma(L2deriv = L2deriv, risk = risk, neighbor = neighbor,
biastype = biastype, cent = cent, clip = clip)
solvfct <- function(r){
mse <- r^2 *clip^2 + s
mse4 <- (r^2 *clip^2/3 + s)/mse
r^2*clip*mse4 + gamm }
r <- try(uniroot(solvfct, lower=1e-5, upper = 10)\$root,silent=TRUE)
if(is(r, "try-error")) return(NA)
return(r)
})

L2deriv = "UnivariateDistribution",
risk = "asL4",
neighbor = "TotalVarNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
s <- getInfV(L2deriv, neighbor, biastype, clip, cent, stand=1)
gamm <- getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype,
cent = if(symm) -clip/2 else cent , clip = clip)
solvfct <- function(r){
mse <- r^2 *clip^2 + s
mse4 <- (r^2 *clip^2/3 + s)/mse
r^2*clip*mse4 + gamm }
r <- try(uniroot(solvfct, lower=1e-5, upper = 10)\$root,silent=TRUE)
if(is(r, "try-error")) return(NA)
return(r)
})

###############################################################################
## optimal radius for given clipping bound for asymptotic under-/overshoot risk
###############################################################################
L2deriv = "UnivariateDistribution",
risk = "asUnOvShoot",
neighbor = "UncondNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
gamm <- getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype,
cent = if(symm) -clip/2 else cent , clip = clip)
return( -gamm*risk@width)
})

###############################################################################
## optimal radius for given clipping bound for asymptotic semivariance
###############################################################################
L2deriv = "UnivariateDistribution",
risk = "asSemivar",
neighbor = "ContNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype, cent,  symm, trafo){
biastype <- if(sign(risk)==1) positiveBias() else negativeBias()
z0 <- getInfCent(L2deriv = L2deriv, risk = risk, neighbor = neighbor,
biastype = biastype,
clip = max(clip, 1e-4), cent = 0, trafo = trafo,
symm = symm, tol.z = 1e-6)

ga <- getInfGamma(L2deriv = L2deriv, risk = risk, neighbor = neighbor,
biastype = biastype, cent = cent, clip = clip)

solvfct <- function(r){
si <- if (sign(risk)>0) 1 else -1
v0 <- E(L2deriv, function(x) pmin( x-z0,  si*clip)^2 )
s0 <- sqrt(v0)
sv <- r * clip / s0
er <- r^2 * clip + r * s0 * dnorm(sv) / pnorm(sv) + ga
return(er)
}
r <- try(uniroot(solvfct, lower=1e-5, upper = 10)\$root,silent=TRUE)
if(is(r, "try-error")) return(NA)
return(r)
})
```

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ROptEst documentation built on April 6, 2019, 3:01 a.m.