Generic function for the computation of optimally robust ICs.
optIC(model, risk, ...)# S4 method for InfRobModel,asRisk
optIC(model, risk, z.start = NULL, A.start = NULL,
upper = 1e4, lower = 1e-4,
OptOrIter = "iterate", maxiter = 50,
tol = .Machine$double.eps^0.4, warn = TRUE,
noLow = FALSE, verbose = NULL, ...,
.withEvalAsVar = TRUE, withMakeIC = FALSE,
returnNAifProblem = FALSE, modifyICwarn = NULL)
# S4 method for InfRobModel,asUnOvShoot
optIC(model, risk, upper = 1e4,
lower = 1e-4, maxiter = 50,
tol = .Machine$double.eps^0.4,
withMakeIC = FALSE, warn = TRUE,
verbose = NULL, modifyICwarn = NULL, ...)
# S4 method for FixRobModel,fiUnOvShoot
optIC(model, risk, sampleSize, upper = 1e4, lower = 1e-4,
maxiter = 50, tol = .Machine$double.eps^0.4,
withMakeIC = FALSE, warn = TRUE,
Algo = "A", cont = "left",
verbose = NULL, modifyICwarn = NULL, ...)
Some optimally robust IC is computed.
probability model.
object of class "RiskType".
additional arguments; e.g. are passed on to E via
e.g. makeIC in case of all signature,
and, in addition, to getInfRobIC in case of
signature("InfRobModel","asRisk").
initial value for the centering constant.
initial value for the standardizing matrix.
upper bound for the optimal clipping bound.
lower bound for the optimal clipping bound.
the maximum number of iterations.
the desired accuracy (convergence tolerance).
logical: print warnings.
integer: sample size.
"A" or "B".
"left" or "right".
logical: is lower case to be computed?
character; which method to be used for determining Lagrange
multipliers A and a: if (partially) matched to "optimize",
getLagrangeMultByOptim is used; otherwise: by default, or if matched to
"iterate" or to "doubleiterate",
getLagrangeMultByIter is used. More specifically,
when using getLagrangeMultByIter, and if argument risk is of
class "asGRisk", by default and if matched to "iterate"
we use only one (inner) iteration, if matched to "doubleiterate"
we use up to Maxiter (inner) iterations.
logical: if TRUE, some messages are printed.
logical (of length 1):
if TRUE, risks based on covariances are to be
evaluated (default), otherwise just a call is returned.
logical; if TRUE the [p]IC is passed through
makeIC before return.
logical (of length 1):
if TRUE (not the default), in case of convergence problems in
the algorithm, returns NA.
logical: should a (warning) information be added if
modifyIC is applied and hence some optimality information could
no longer be valid? Defaults to NULL in which case this value
is taken from RobAStBaseOptions.
computes optimally robust influence curve for robust models with infinitesimal neighborhoods and various asymptotic risks.
computes optimally robust influence curve for robust models with infinitesimal neighborhoods and asymptotic under-/overshoot risk.
computes optimally robust influence curve for robust models with fixed neighborhoods and finite-sample under-/overshoot risk.
Matthias Kohl Matthias.Kohl@stamats.de
In case of the finite-sample risk "fiUnOvShoot" one can choose
between two algorithms for the computation of this risk where the least favorable
contamination is assumed to be left or right of some bound. For more details
we refer to Section 11.3 of Kohl (2005).
Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269--278.
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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1007/s10260-010-0133-0").
Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106--115.
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer. tools:::Rd_expr_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. tools:::Rd_expr_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 tools:::Rd_expr_doi("10.18452/3638").
InfluenceCurve-class, RiskType-class
B <- BinomFamily(size = 25, prob = 0.25)
## classical optimal IC
IC0 <- optIC(model = B, risk = asCov())
plot(IC0) # plot IC
checkIC(IC0, B)
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