roptest {ROptEst} | R Documentation |
Optimally robust estimation
Description
Function to compute optimally robust estimates for L2-differentiable parametric families via k-step construction.
Usage
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)
Arguments
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 k-steps construction |
distance |
distance function used in |
startPar |
initial information used by |
verbose |
logical: if |
useLast |
which parameter estimate (initial estimate or
k-step estimate) shall be used to fill the slots |
OptOrIter |
character; which method to be used for determining Lagrange
multipliers |
withUpdateInKer |
if there is a non-trivial trafo in the model with matrix |
IC.UpdateInKer |
if there is a non-trivial trafo in the model with matrix |
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 |
Details
Computes the optimally robust estimator for a given L2 differentiable
parametric family. The computation uses a k-step 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 radius-minimax estimator in sense of
Rieder et al. (2001, 2008), respectively Section 2.2 of Kohl (2005) is returned.
Finite-sample 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 finite-sample
corrected (enlarged) radius based on the results of large Monte-Carlo
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 Minimum-Distance 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 re-computed using the value of the one-step 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 k-step 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
.
Value
Object of class "kStepEstimate"
. In addition, it has
an attribute "timings"
where computation time is stored.
Author(s)
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
References
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.
Kohl, M. and Ruckdeschel, P. (2010): R package distrMod: Object-Oriented Implementation of Probability Models. J. Statist. Softw. 35(10), 1–27. doi:10.18637/jss.v035.i10.
Kohl, M. and Ruckdeschel, P., and Rieder, H. (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333–354. doi:10.1007/s10260-010-0133-0.
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer. doi:10.1007/978-1-4684-0624-5.
Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications 17(1) 13-40. doi:10.1007/s10260-007-0047-7.
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 doi:10.18452/3638
See Also
roblox
,
L2ParamFamily-class
UncondNeighborhood-class
,
RiskType-class
Examples
## 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=(1-ind)*0.25 + ind*0.9)
## ML-estimate
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: Rutherford-Geiger (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))
## ML-estimate
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
#############################
## this example of a two dimensional parameter
## to be estimated will need more time than
## 5 seconds to run
## you can find it in
## system.file("scripts", "examples_taking_longer.R",
## package="ROptEst")