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

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

setMethod("getInfClip", signature(clip = "numeric",
L2deriv = "UnivariateDistribution",
risk = "asMSE",
neighbor = "ContNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
getInfGamma(L2deriv = L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = cent, clip = clip))
})

setMethod("getInfClip", signature(clip = "numeric",
L2deriv = "UnivariateDistribution",
risk = "asMSE",
neighbor = "TotalVarNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
if(symm){
getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = -clip/2, clip = clip))
}else{
getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = cent, clip = clip))
}
})

setMethod("getInfClip", signature(clip = "numeric",
L2deriv = "EuclRandVariable",
risk = "asMSE",
neighbor = "UncondNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
Distr, stand, cent, trafo, ...){
getInfGamma(L2deriv = L2deriv, risk = risk, neighbor = neighbor,
biastype = biastype, Distr = Distr, stand = stand,
cent = cent, clip = clip, ...))
})

###############################################################################
## optimal clipping bound for asymptotic L1risk
###############################################################################

setMethod("getInfClip", signature(clip = "numeric",
L2deriv = "UnivariateDistribution",
risk = "asL1",
neighbor = "ContNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
s <- getInfV(L2deriv, neighbor, biastype, clip, cent, stand=1)
w <- r * clip / s^.5
dp <- 2*dnorm(w)
pp <- 2*pnorm(w)-1
return(s^.5*r*pp/dp +
getInfGamma(L2deriv = L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = cent, clip = clip))
})

setMethod("getInfClip", signature(clip = "numeric",
L2deriv = "UnivariateDistribution",
risk = "asL1",
neighbor = "TotalVarNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
s <- getInfV(L2deriv, neighbor, biastype, clip, cent, stand=1)
w <- r * clip / s^.5
dp <- 2*dnorm(w)
pp <- 2*pnorm(w)-1
lhs <- s^.5*r*pp/dp
if(symm){
return(lhs +
getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = -clip/2, clip = clip))
}else{
return(lhs +
getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = cent, clip = clip))
}
})

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

setMethod("getInfClip", signature(clip = "numeric",
L2deriv = "UnivariateDistribution",
risk = "asL4",
neighbor = "ContNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
s <- getInfV(L2deriv, neighbor, biastype, clip, cent, stand=1)
mse <- r^2 *clip^2 + s
mse4 <- (r^2 *clip^2/3 + s)/mse
return(r^2*clip*mse4 +
getInfGamma(L2deriv = L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = cent, clip = clip))
})

setMethod("getInfClip", signature(clip = "numeric",
L2deriv = "UnivariateDistribution",
risk = "asL4",
neighbor = "TotalVarNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
s <- getInfV(L2deriv, neighbor, biastype, clip, cent, stand=1)
mse <- r^2 *clip^2 + s
mse4 <- (r^2 *clip^2/3 + s)/mse
if(symm){
return(r^2*clip*mse4 +
getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = -clip/2, clip = clip))
}else{
return(r^2*clip*mse4 +
getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = cent, clip = clip))
}
})

###############################################################################
## optimal clipping bound for asymptotic under-/overshoot risk
###############################################################################
setMethod("getInfClip", signature(clip = "numeric",
L2deriv = "UnivariateDistribution",
risk = "asUnOvShoot",
neighbor = "UncondNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype,
cent, symm, trafo){
if(symm){
getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = -clip/2, clip = clip))
}else{
getInfGamma(L2deriv = sign(as.vector(trafo))*L2deriv, risk = risk,
neighbor = neighbor, biastype = biastype, cent = cent, clip = clip))
}
})

###############################################################################
## optimal clipping bound for asymptotic semivariance
###############################################################################
setMethod("getInfClip", signature(clip = "numeric",
L2deriv = "UnivariateDistribution",
risk = "asSemivar",
neighbor = "ContNeighborhood"),
function(clip, L2deriv, risk, neighbor, biastype, cent,  symm, trafo, ...){

dotsI <- .filterEargsWEargList(list(...))
if(is.null(dotsI\$useApply)) dotsI\$useApply <- FALSE

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)

if (sign(risk)>0)
v0 <- do.call(E,c(list(L2deriv, function(x) pmin( x-z0,  clip)^2),dotsI))
else
v0 <- do.call(E,c(list(L2deriv, function(x) pmax( x-z0, -clip)^2),dotsI))

s0 <- sqrt(v0)
sv <- r * clip / s0

er <- r^2 * clip + r * s0 * dnorm(sv) / pnorm(sv) + ga
return(er)
})
```

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ROptEst documentation built on May 2, 2019, 5:45 p.m.