Nothing
###############################################################################
## Example: Exponential Scale Family
###############################################################################
require(ROptEst)
options("newDevice"=TRUE)
## generates Exponential Scale Family with scale = 0.5 (rate = 2)
E1 <- ExpScaleFamily(scale = 0.5)
E1 # show E1
#An object of class "ExpScaleFamily"
#### name: Exponential scale family
#
#### distribution: Distribution Object of Class: Exp
# rate: 2
#
#### param: An object of class "ParamFamParameter"
#name: scale
#scale: 0.5
#fixed part of param.:
# : 0
#trafo:
# scale
#scale 1
#
#### props:
#[1] "The Exponential scale family is invariant under"
#[2] "the group of transformations 'g(y) = scale*y'"
#[3] "with scale parameter 'scale'"
plot(E1) # plot of Exp(rate = 1) and L_2 derivative
checkL2deriv(E1)
#precision of centering: -3.023619e-06
#precision of Fisher information:
# scale
#scale -0.0001047172
#$maximum.deviation
#[1] 0.0001047172
## classical optimal IC
E1.IC0 <- optIC(model = E1, risk = asCov())
E1.IC0 # show IC
#An object of class IC
#### name: Classical optimal influence curve for Exponential scale family
#### L2-differentiable parametric family: Exponential scale family
#
#### 'Curve': An object of class EuclRandVarList
#Domain: Real Space with dimension 1
#[[1]]
#length of Map: 1
#Range: Real Space with dimension 1
#
#### Infos:
# method message
#[1,] "optIC" "optimal IC in sense of Cramer-Rao bound"
checkIC(E1.IC0)
#precision of centering: -7.559048e-07
#precision of Fisher consistency:
# scale
#scale -2.61793e-05
#maximum deviation
# 2.61793e-05
Risks(E1.IC0)
#$asCov
# scale
#scale 0.25
#
#$trAsCov
#[1] 0.25
plot(E1.IC0) # plot IC
## L_2 family + infinitesimal neighborhood
E1.Rob1 <- InfRobModel(center = E1, neighbor = ContNeighborhood(radius = 0.5))
E1.Rob1 # show E1.Rob1
#An object of class InfRobModel
####### center: An object of class "ExpScaleFamily"
#### name: Exponential scale family
#
#### distribution: Distribution Object of Class: Exp
# rate: 2
#
#### param: An object of class "ParamFamParameter"
#name: scale
#scale: 0.5
#fixed part of param.:
# : 0
#trafo:
# scale
#scale 1
#
#### props:
#[1] "The Exponential scale family is invariant under"
#[2] "the group of transformations 'g(y) = scale*y'"
#[3] "with scale parameter 'scale'"
#
####### neighborhood: An object of class ContNeighborhood
#type: (uncond.) convex contamination neighborhood
#radius: 0.5
(E1.Rob2 <- InfRobModel(center = E1, neighbor = TotalVarNeighborhood(radius = 0.5)))
#An object of class InfRobModel
####### center: An object of class "ExpScaleFamily"
#### name: Exponential scale family
#
#### distribution: Distribution Object of Class: Exp
# rate: 2
#
#### param: An object of class "ParamFamParameter"
#name: scale
#scale: 0.5
#fixed part of param.:
# : 0
#trafo:
# scale
#scale 1
#
#### props:
#[1] "The Exponential scale family is invariant under"
#[2] "the group of transformations 'g(y) = scale*y'"
#[3] "with scale parameter 'scale'"
#
####### neighborhood: An object of class TotalVarNeighborhood
#type: (uncond.) total variation neighborhood
#radius: 0.5
## MSE solution
(E1.IC1 <- optIC(model=E1.Rob1, risk=asMSE()))
#An object of class ContIC
#### name: IC of contamination type
#
#### L2-differentiable parametric family: Exponential scale family
#### param: An object of class "ParamFamParameter"
#name: scale
#scale: 0.5
#fixed part of param.:
# : 0
#trafo:
# scale
#scale 1
#
### neighborhood radius: 0.5
#
#### clip: [1] 0.8449229
#### cent: [1] -0.2112307
#### stand:
# scale
#scale 0.5249744
#
#### Infos:
# method message
#[1,] "optIC" "optimally robust IC for asMSE"
checkIC(E1.IC1)
#precision of centering: -2.924022e-05
#precision of Fisher consistency:
# scale
#scale -1.068126e-05
#maximum deviation
# 2.924022e-05
Risks(E1.IC1)
#$asCov
# scale
#scale 0.3465008
#
#$asBias
#$asBias$value
#[1] 0.8449229
#
#$asBias$biastype
#An object of class symmetricBias
#Slot "name":
#[1] "symmetric Bias"
#
#
#$asBias$normtype
#An object of class NormType
#Slot "name":
#[1] "EuclideanNorm"
#
#Slot "fct":
#function (x)
#{
# if (is.vector(x))
# return(abs(x))
# else return(sqrt(colSums(x^2)))
#}
#<environment: namespace:distrMod>
#
#
#$asBias$neighbortype
#[1] "ContNeighborhood"
#attr(,"package")
#[1] "RobAStBase"
#
#
#$trAsCov
#$trAsCov$value
# scale
#scale 0.3465008
#
#$trAsCov$normtype
#An object of class NormType
#Slot "name":
#[1] "EuclideanNorm"
#
#Slot "fct":
#function (x)
#{
# if (is.vector(x))
# return(abs(x))
# else return(sqrt(colSums(x^2)))
#}
#<environment: namespace:distrMod>
#
#
#
#$asMSE
#$asMSE$value
# scale
#scale 0.5249744
#
#$asMSE$r
#[1] 0.5
#
#$asMSE$at
#An object of class ContNeighborhood
#type: (uncond.) convex contamination neighborhood
#radius: 0.5
plot(E1.IC1)
(E1.IC2 <- optIC(model=E1.Rob2, risk=asMSE()))
checkIC(E1.IC2)
Risks(E1.IC2)
plot(E1.IC2)
## lower case solutions
(E1.IC3 <- optIC(model=E1.Rob1, risk=asBias()))
checkIC(E1.IC3)
Risks(E1.IC3)
plot(E1.IC3)
(E1.IC4 <- optIC(model=E1.Rob2, risk=asBias()))
checkIC(E1.IC4)
Risks(E1.IC4)
plot(E1.IC4)
## Hampel solution
(E1.IC5 <- optIC(model=E1.Rob1, risk=asHampel(bound=clip(E1.IC1))))
checkIC(E1.IC5)
Risks(E1.IC5)
plot(E1.IC5)
(E1.IC6 <- optIC(model=E1.Rob2, risk=asHampel(bound=Risks(E1.IC2)$asBias$value), maxiter = 200))
checkIC(E1.IC6)
Risks(E1.IC6)
plot(E1.IC6)
## radius minimax IC
(E1.IC7 <- radiusMinimaxIC(L2Fam=E1, neighbor=ContNeighborhood(), risk=asMSE(), loRad=0, upRad=0.5))
checkIC(E1.IC7)
Risks(E1.IC7)
(E1.IC8 <- radiusMinimaxIC(L2Fam=E1, neighbor=TotalVarNeighborhood(), risk=asMSE(), loRad=0, upRad=0.5))
checkIC(E1.IC8)
Risks(E1.IC8)
## least favorable radius
## (may take quite some time!)
(E1.r.rho1 <- leastFavorableRadius(L2Fam=E1, neighbor=ContNeighborhood(),
risk=asMSE(), rho=0.5))
(E1.r.rho2 <- leastFavorableRadius(L2Fam=E1, neighbor=TotalVarNeighborhood(),
risk=asMSE(), rho=1/3))
## one-step estimation
## We use contamination neighborhoods but could also use total variation
## neighborhoods
## 1. generate a contaminated sample
ind <- rbinom(1e2, size=1, prob=0.05)
E1.x <- rexp(1e2, rate=(1-ind)*2+ind*10)
## 2.1 Kolmogorov(-Smirnov) minimum distance estimator
(E1.est01 <- MDEstimator(x=E1.x, ExpScaleFamily()))
## 2.2 Cramer-von-Mises minimum distance estimator
(E1.est02 <- MDEstimator(x=E1.x, ExpScaleFamily(), distance = CvMDist))
## 3. k-step estimation: radius known
E1.Rob31 <- InfRobModel(center=ExpScaleFamily(scale=estimate(E1.est01)),
neighbor=ContNeighborhood(radius=0.5))
E1.IC9 <- optIC(model=E1.Rob31, risk=asMSE())
(E1.est11 <- oneStepEstimator(E1.x, IC=E1.IC9, start=E1.est01))
(E1.est12 <- kStepEstimator(E1.x, IC=E1.IC9, start=E1.est01, steps = 3))
## its simpler to use function roptest
(E1.est13 <- roptest(E1.x, ExpScaleFamily(), eps = 0.05, distance = KolmogorovDist,
steps = 3))
E1.Rob32 <- InfRobModel(center=ExpScaleFamily(scale=estimate(E1.est02)),
neighbor=ContNeighborhood(radius=0.5))
E1.IC10 <- optIC(model=E1.Rob32, risk=asMSE())
(E1.est21 <- oneStepEstimator(E1.x, IC=E1.IC10, start=E1.est02))
(E1.est22 <- kStepEstimator(E1.x, IC=E1.IC10, start=E1.est02, steps = 3))
## its simpler to use function roptest
(E1.est23 <- roptest(E1.x, ExpScaleFamily(), eps = 0.05, steps = 3))
## comparison
estimate(E1.est11)
estimate(E1.est12)
estimate(E1.est13)
estimate(E1.est21)
estimate(E1.est22)
estimate(E1.est23)
## confidence intervals
confint(E1.est11, symmetricBias())
confint(E1.est12, symmetricBias())
confint(E1.est13, symmetricBias())
confint(E1.est21, symmetricBias())
confint(E1.est22, symmetricBias())
confint(E1.est23, symmetricBias())
## 4. one-step estimation: radius interval
E1.IC11 <- radiusMinimaxIC(L2Fam=ExpScaleFamily(scale=estimate(E1.est01)),
neighbor=ContNeighborhood(), risk=asMSE(), loRad=0, upRad=Inf)
(E1.est31 <- oneStepEstimator(E1.x, IC=E1.IC11, start=E1.est01))
(E1.est32 <- kStepEstimator(E1.x, IC=E1.IC11, start=E1.est01, steps = 3))
## its simpler to use function roptest
(E1.est33 <- roptest(E1.x, ExpScaleFamily(), eps.upper = 0.5, distance = KolmogorovDist,
steps = 3))
E1.IC12 <- radiusMinimaxIC(L2Fam=ExpScaleFamily(scale=estimate(E1.est02)),
neighbor=ContNeighborhood(), risk=asMSE(), loRad=0, upRad=Inf)
(E1.est41 <- oneStepEstimator(E1.x, IC=E1.IC12, start=E1.est02))
(E1.est42 <- kStepEstimator(E1.x, IC=E1.IC12, start=E1.est02, steps = 3))
## its simpler to use function roptest
(E1.est43 <- roptest(E1.x, ExpScaleFamily(), eps.upper = 0.5, steps = 3))
## comparison
estimate(E1.est31)
estimate(E1.est32)
estimate(E1.est33)
estimate(E1.est41)
estimate(E1.est42)
estimate(E1.est43)
## confidence intervals
confint(E1.est31, symmetricBias())
confint(E1.est32, symmetricBias())
confint(E1.est33, symmetricBias())
confint(E1.est41, symmetricBias())
confint(E1.est42, symmetricBias())
confint(E1.est43, symmetricBias())
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.