Description Usage Arguments Details Value Author(s) References See Also Examples
These are wrapper functions to 'roptest' to compute optimally robust estimates, more specifically RMXEs, OMSEs, MBREs, and OBREs, 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 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44  RMXEstimator(x, L2Fam, fsCor = 1, initial.est, neighbor = ContNeighborhood(),
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)
OMSEstimator(x, L2Fam, eps=0.5, fsCor = 1, initial.est, neighbor = ContNeighborhood(),
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)
OBREstimator(x, L2Fam, eff=0.95, fsCor = 1, initial.est, neighbor = ContNeighborhood(),
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)
MBREstimator(x, L2Fam, fsCor = 1, initial.est, neighbor = ContNeighborhood(),
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)

x 
sample 
L2Fam 
object of class 
eff 
positive real (0 <= 
eps 
positive real (0 < 
fsCor 
positive real: factor used to correct the neighborhood radius; see details. 
initial.est 
initial estimate for unknown parameter. If missing minimum distance estimator is computed. 
neighbor 
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 
The functions compute optimally robust estimator for a given L2 differentiable
parametric family; more specifically they are RMXEs, OMSEs, MBREs, and OBREs.
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).
For OMSE, i.e., the asymptotically linear estimator with minimax mean squared
error on this neighborhood of given size, the amount of gross errors
(contamination) is assumed to be known, and is 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, RMXE should be used, i.e., the radiusminimax estimator in the sense of Rieder et al. (2001, 2008), respectively Section 2.2 of Kohl (2005) is returned.
The OBRE, i.e., the optimal biasrobust (asymptotically linear) estimator; (terminology due to Hampel et al (1985)), expects an efficiency loss (at the ideal model) to be specified and then, according to an (asymptotic) Anscombe criterion computes the the bias bound achieving this efficiency loss.
The MBRE, i.e., the most biasrobust (asymptotically linear) estimator; (terminology due to Hampel et al (1985)), uses the influence curve with minimal possible bias bound, hence minimaxes bias on these neighborhoods (in an infinitesimal sense)..
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 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.
All these estimators are realized as wrappers to function roptest
.
Timings for the steps run through in these estimators 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 the estimator function, 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 [email protected],
Peter Ruckdeschel [email protected]
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
roptest
, robest
,
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  #############################
## 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
MLE.bin < MLEstimator(x, BinomFamily(size = 25))
## compute optimally robust estimators
OMSE.bin < OMSEstimator(x, BinomFamily(size = 25), steps = 3)
MBRE.bin < MBREstimator(x, BinomFamily(size = 25), steps = 3)
estimate(MLE.bin)
estimate(MBRE.bin)
estimate(OMSE.bin)
## to reduce time load at CRAN tests
RMXE.bin < RMXEstimator(x, BinomFamily(size = 25), steps = 3)
OBRE.bin < OBREstimator(x, BinomFamily(size = 25), steps = 3)
estimate(RMXE.bin)
estimate(OBRE.bin)
## to reduce time load at CRAN tests
#############################
## 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
MLE.pois < MLEstimator(x, PoisFamily())
OBRE.pois < OBREstimator(x, PoisFamily(), steps = 3)
OMSE.pois < OMSEstimator(x, PoisFamily(), steps = 3)
MBRE.pois < MBREstimator(x, PoisFamily(), steps = 3)
RMXE.pois < RMXEstimator(x, PoisFamily(), steps = 3)
estimate(MLE.pois)
estimate(OBRE.pois)
estimate(RMXE.pois)
estimate(MBRE.pois)
estimate(OMSE.pois)
## to reduce time load at CRAN tests
#############################
## 3. Normal (Gaussian) location and scale
#############################
## 24 determinations of copper in wholemeal flour
library(MASS)
data(chem)
MLE.n < MLEstimator(chem, NormLocationScaleFamily())
MBRE.n < MBREstimator(chem, NormLocationScaleFamily(), steps = 3)
OMSE.n < OMSEstimator(chem, NormLocationScaleFamily(), steps = 3)
OBRE.n < OBREstimator(chem, NormLocationScaleFamily(), steps = 3)
RMXE.n < RMXEstimator(chem, NormLocationScaleFamily(), steps = 3)
estimate(MLE.n)
estimate(MBRE.n)
estimate(OMSE.n)
estimate(OBRE.n)
estimate(RMXE.n)

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