Description Usage Arguments Details Value Author(s) References See Also Examples
Function to compute optimally robust estimates for L2differentiable parametric families via kstep construction.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  roptest(x, L2Fam, eps, eps.lower, eps.upper, fsCor = 1, initial.est,
neighbor = ContNeighborhood(), risk = asMSE(), steps = 1L,
distance = CvMDist, startPar = NULL, verbose = NULL,
OptOrIter = "iterate",
useLast = getRobAStBaseOption("kStepUseLast"),
withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
withICList = getRobAStBaseOption("withICList"),
withPICList = getRobAStBaseOption("withPICList"),
na.rm = TRUE, initial.est.ArgList, ...,
withLogScale = TRUE, ..withCheck = FALSE, withTimings = FALSE,
withMDE = NULL, withEvalAsVar = NULL, withMakeIC = FALSE,
modifyICwarn = NULL, E.argList = NULL, diagnostic = FALSE)
roptest.old(x, L2Fam, eps, eps.lower, eps.upper, fsCor = 1, initial.est,
neighbor = ContNeighborhood(), risk = asMSE(), steps = 1L,
distance = CvMDist, startPar = NULL, verbose = NULL,
OptOrIter = "iterate",
useLast = getRobAStBaseOption("kStepUseLast"),
withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
withICList = getRobAStBaseOption("withICList"),
withPICList = getRobAStBaseOption("withPICList"),
na.rm = TRUE, initial.est.ArgList, ...,
withLogScale = TRUE)

x 
sample 
L2Fam 
object of class 
eps 
positive real (0 < 
eps.lower 
positive real (0 <= 
eps.upper 
positive real ( 
fsCor 
positive real: factor used to correct the neighborhood radius; see details. 
initial.est 
initial estimate for unknown parameter. If missing, a minimum distance estimator is computed. 
neighbor 
object of class 
risk 
object of class 
steps 
positive integer: number of steps used for ksteps construction 
distance 
distance function used in 
startPar 
initial information used by 
verbose 
logical: if 
useLast 
which parameter estimate (initial estimate or
kstep estimate) shall be used to fill the slots 
OptOrIter 
character; which method to be used for determining Lagrange
multipliers 
withUpdateInKer 
if there is a nontrivial trafo in the model with matrix D, shall the parameter be updated on ker(D)? 
IC.UpdateInKer 
if there is a nontrivial trafo in the model with matrix D,
the IC to be used for this; if 
withPICList 
logical: shall slot 
withICList 
logical: shall slot 
na.rm 
logical: if 
initial.est.ArgList 
a list of arguments to be given to argument 
... 
further arguments 
withLogScale 
logical; shall a scale component (if existing and found
with name 
..withCheck 
logical: if 
withTimings 
logical: if 
withMDE 
logical or 
withEvalAsVar 
logical or 
withMakeIC 
logical; if 
modifyICwarn 
logical: should a (warning) information be added if

E.argList 

diagnostic 
logical; if 
Computes the optimally robust estimator for a given L2 differentiable
parametric family. The computation uses a kstep construction with an
appropriate initial estimate; cf. also kStepEstimator
.
Valid candidates are e.g. Kolmogorov(Smirnov) or von Mises minimum
distance estimators (default); cf. Rieder (1994) and Kohl (2005).
Before package version 0.9, this computation was done with the code of
function roptest.old
(with the same formals). From package version
0.9 on, this function uses the modularized function robest
internally.
If the amount of gross errors (contamination) is known, it can be
specified by eps
. The radius of the corresponding infinitesimal
contamination neighborhood is obtained by multiplying eps
by the square root of the sample size.
If the amount of gross errors (contamination) is unknown, try to find a
rough estimate for the amount of gross errors, such that it lies
between eps.lower
and eps.upper
.
In case eps.lower
is specified and eps.upper
is missing,
eps.upper
is set to 0.5. In case eps.upper
is specified and
eps.lower
is missing, eps.lower
is set to 0.
If neither eps
nor eps.lower
and/or eps.upper
is
specified, eps.lower
and eps.upper
are set to 0 and 0.5,
respectively.
If eps
is missing, the radiusminimax estimator in sense of
Rieder et al. (2001, 2008), respectively Section 2.2 of Kohl (2005) is returned.
Finitesample and higher order results suggest that the asymptotically
optimal procedure is to liberal. Using fsCor
the radius can be
modified  as a rule enlarged  to obtain a more conservative estimate.
In case of normal location and scale there is function
finiteSampleCorrection
which returns a finitesample
corrected (enlarged) radius based on the results of large MonteCarlo
studies.
The logic in argument initial.est
is as follows: It can be
a numeric vector of the length of the unknow parameter or a function or
it can be missing. If it is missing, one consults argument startPar
for a search interval (if a one dimensional unknown parameter) or a starting
value for the search (if the dimension of the unknown parameter is larger
than one). If startPar
is missing, too, it takes the value from
the corresponding slot of argument L2Fam
. Then, if argument withMDE
is TRUE
a MinimumDistance estimator is computed as initial value
initial.est
with distance as specified in argument distance
and possibly further arguments as passed through ...
.
In the next step, the value of initial.est
(either if not missing
from beginning or as computed through the MDE) is then passed on to
kStepEstimator.start
which then takes out the essential
information for the sequel, i.e., a numeric vector of the estimate.
At this initial value the optimal influence curve is computed through
interface getStartIC
, which in turn, depending on the risk calls
optIC
, radiusMinimaxIC
, or computes the IC
from precomputed grid values in case of risk
being of class
interpolRisk
. With the obtained optimal IC, kStepEstimator
is called.
The default value of argument useLast
is set by the
global option kStepUseLast
which by default is set to
FALSE
. In case of general models useLast
remains unchanged during the computations. However, if
slot CallL2Fam
of IC
generates an object of
class "L2GroupParamFamily"
the value of useLast
is changed to TRUE
.
Explicitly setting useLast
to TRUE
should
be done with care as in this situation the influence curve
is recomputed using the value of the onestep estimate
which may take quite a long time depending on the model.
If useLast
is set to TRUE
the computation of asvar
,
asbias
and IC
is based on the kstep estimate.
Timings for the steps run through in roptest
are available
in attributes timings
, and for the step of the
kStepEstimator
in kStepTimings
.
One may also use the arguments startCtrl
, startICCtrl
, and
kStepCtrl
of function robest
. This allows for individual
settings of E.argList
, withEvalAsVar
, and
withMakeIC
for the different steps. If any of the three arguments
startCtrl
, startICCtrl
, and kStepCtrl
is used, the
respective attributes set in the correspondig argument are used and, if
colliding with arguments directly passed to roptest
, the directly
passed ones are ignored.
Diagnostics on the involved integrations are available if argument
diagnostic
is TRUE
. Then there are attributes diagnostic
and kStepDiagnostic
attached to the return value, which may be inspected
and assessed through showDiagnostic
and
getDiagnostic
.
Object of class "kStepEstimate"
. In addition, it has
an attribute "timings"
where computation time is stored.
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@unioldenburg.de
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
Kohl, M. and Ruckdeschel, P. (2010): R package distrMod: ObjectOriented Implementation of Probability Models. J. Statist. Softw. 35(10), 1–27
Kohl, M. and Ruckdeschel, P., and Rieder, H. (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333–354.
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications 17(1) 1340.
Rieder, H., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under www.unibayreuth.de/departments/math/org/mathe7/RIEDER/pubs/RR.pdf
roblox
,
L2ParamFamilyclass
UncondNeighborhoodclass
,
RiskTypeclass
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129  ## Don't run to reduce check time on CRAN
## Not run:
#############################
## 1. Binomial data
#############################
## generate a sample of contaminated data
set.seed(123)
ind < rbinom(100, size=1, prob=0.05)
x < rbinom(100, size=25, prob=(1ind)*0.25 + ind*0.9)
## MLestimate
MLest < MLEstimator(x, BinomFamily(size = 25))
estimate(MLest)
confint(MLest)
## compute optimally robust estimator (known contamination)
robest1 < roptest(x, BinomFamily(size = 25), eps = 0.05, steps = 3)
robest1.0 < roptest.old(x, BinomFamily(size = 25), eps = 0.05, steps = 3)
identical(robest1,robest1.0)
estimate(robest1)
confint(robest1, method = symmetricBias())
## neglecting bias
confint(robest1)
plot(pIC(robest1))
tmp < qqplot(x, robest1, cex.pch=1.5, exp.cex2.pch = .25,
exp.fadcol.pch = .55, jit.fac=.9)
## compute optimally robust estimator (unknown contamination)
robest2 < roptest(x, BinomFamily(size = 25), eps.lower = 0, eps.upper = 0.2, steps = 3)
estimate(robest2)
confint(robest2, method = symmetricBias())
plot(pIC(robest2))
## total variation neighborhoods (known deviation)
robest3 < roptest(x, BinomFamily(size = 25), eps = 0.025,
neighbor = TotalVarNeighborhood(), steps = 3)
estimate(robest3)
confint(robest3, method = symmetricBias())
plot(pIC(robest3))
## total variation neighborhoods (unknown deviation)
robest4 < roptest(x, BinomFamily(size = 25), eps.lower = 0, eps.upper = 0.1,
neighbor = TotalVarNeighborhood(), steps = 3)
estimate(robest4)
confint(robest4, method = symmetricBias())
plot(pIC(robest4))
#############################
## 2. Poisson data
#############################
## Example: RutherfordGeiger (1910); cf. Feller~(1968), Section VI.7 (a)
x < c(rep(0, 57), rep(1, 203), rep(2, 383), rep(3, 525), rep(4, 532),
rep(5, 408), rep(6, 273), rep(7, 139), rep(8, 45), rep(9, 27),
rep(10, 10), rep(11, 4), rep(12, 0), rep(13, 1), rep(14, 1))
## MLestimate
MLest < MLEstimator(x, PoisFamily())
estimate(MLest)
confint(MLest)
## compute optimally robust estimator (unknown contamination)
robest < roptest(x, PoisFamily(), eps.upper = 0.1, steps = 3)
estimate(robest)
confint(robest, symmetricBias())
plot(pIC(robest))
tmp < qqplot(x, robest, cex.pch=1.5, exp.cex2.pch = .25,
exp.fadcol.pch = .55, jit.fac=.9)
## total variation neighborhoods (unknown deviation)
robest1 < roptest(x, PoisFamily(), eps.upper = 0.05,
neighbor = TotalVarNeighborhood(), steps = 3)
estimate(robest1)
confint(robest1, symmetricBias())
plot(pIC(robest1))
## End(Not run)
#############################
## 3. Normal (Gaussian) location and scale
#############################
## 24 determinations of copper in wholemeal flour
library(MASS)
data(chem)
plot(chem, main = "copper in wholemeal flour", pch = 20)
## MLestimate
MLest < MLEstimator(chem, NormLocationScaleFamily())
estimate(MLest)
confint(MLest)
## Don't run to reduce check time on CRAN
## compute optimally robust estimator (known contamination)
## takes some time > you can use package RobLox for normal
## location and scale which is optimized for speed
robest < roptest(chem, NormLocationScaleFamily(), eps = 0.05, steps = 3)
estimate(robest)
confint(robest, symmetricBias())
plot(pIC(robest))
## plot of relative and absolute information; cf. Kohl (2005)
infoPlot(pIC(robest))
tmp < qqplot(chem, robest, cex.pch=1.5, exp.cex2.pch = .25,
exp.fadcol.pch = .55, withLab = TRUE, which.Order=1:4,
exp.cex2.lbl = .12,exp.fadcol.lbl = .45,
nosym.pCI = TRUE, adj.lbl=c(1.7,.2),
exact.pCI = FALSE, log ="xy")
## finitesample correction
if(require(RobLox)){
n < length(chem)
r < 0.05*sqrt(n)
r.fi < finiteSampleCorrection(n = n, r = r)
fsCor < r.fi/r
robest < roptest(chem, NormLocationScaleFamily(), eps = 0.05,
fsCor = fsCor, steps = 3)
estimate(robest)
}
## compute optimally robust estimator (unknown contamination)
## takes some time > use package RobLox!
robest1 < roptest(chem, NormLocationScaleFamily(), eps.lower = 0.05,
eps.upper = 0.1, steps = 3)
estimate(robest1)
confint(robest1, symmetricBias())
plot(pIC(robest1))
## plot of relative and absolute information; cf. Kohl (2005)
infoPlot(pIC(robest1))

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