These functions are used internally by package ROptEst.
### helper function to check whether given b is in (bmin, bmax)
### if not returns corresponding upper / lower case solution.checkUpLow(L2deriv, b, risk, neighbor, biastype, normtype,
Distr, Finfo, DistrSymm, L2derivSymm,
L2derivDistrSymm, z.start, A.start, trafo, maxiter,
tol, QuadForm, verbose, nrvalpts, warn, ...)
### helper function to return the upper case solution if r=0
.getUpperSol(L2deriv, radius, risk, neighbor, biastype,
normtype, Distr, Finfo, trafo,
QuadForm, verbose, warn, ...)
### helper function to return the lower case solution if b-search was not successful
.getLowerSol(L2deriv, risk, neighbor, Distr, DistrSymm,
L2derivSymm, L2derivDistrSymm,
z.start, A.start, trafo,
maxiter, tol, warn, Finfo, QuadForm, verbose, ...)
### helper function to return upper & lower bounds for b for b-search
.getLowUpB(L2deriv, Finfo, Distr, normtype, z, A, radius, iter)
### helper function to check whether (TotalVariation) weight w has already been modified
.isVirginW(w)
### helper function to check whether (intermediate) results give a pIC
.checkPIC(L2deriv, neighbor, Distr, trafo, z, A, w, z.comp, A.comp, ...)
.LowerCaseMultivariate(L2deriv, neighbor, biastype,
normtype, Distr, Finfo, trafo, z.start = NULL,
A.start = NULL, z.comp = NULL, A.comp = NULL,
maxiter, tol, verbose = NULL, ...)
.LowerCaseMultivariateTV(L2deriv, neighbor, biastype,
normtype, Distr, Finfo, trafo,
A.start, maxiter, tol,
verbose = NULL, ...)
.getSB(IC,neighbor, ...)
a list with items up (logical)
low (logical) and res a return list for
getInfRobIC or NULL: if up is TRUE,
res contains the upper case solution,
if low is TRUE the lower case solution
and if both low and up are FALSE
NULL.
a return list for getInfRobIC
a return list for getInfRobIC
a list with items lower and upper (both numeric).
TRUE or FALSE
nothing is returned; precision values are issued.
a list with elements
erg the return value of the corresponding call to optim,
w the corresponding weight (of class HampelWeight),
normtype the norm ---possibly modified,
z.comp the indices of non-null entries in z.
a list with elements
A the standardization matrix,
b the minimax bias,
w the corresponding weight (of class BdStWeight),
a the corresponding infimum of the [p]IC.
a list with elements s, (the square root of the trace of)
the variance and b, the bias.
L2-derivative of some L2-differentiable family of probability measures.
numeric; clipping bound under consideration.
object of class "RiskType".
object of class "Neighborhood".
object of class "BiasType" --- the bias type with we work.
object of class "NormType" --- the norm type with we work.
object of class "Distribution".
Fisher information matrix.
object of class "DistributionSymmetry".
object of class "FunSymmList".
object of class "DistrSymmList".
initial value for the centering constant.
initial value for the standardizing matrix.
matrix: transformation of the parameter.
the maximum number of iterations.
the desired accuracy (convergence tolerance).
matrix of (or which may coerced to) class
PosSemDefSymmMatrix for use of different
(standardizing) norm
logical: if TRUE, some messages are printed.
integer: number of evaluation points.
logical: print warnings.
radius of the neighborhood.
centering constant (in k-space)
standardizing matrix.
a weight of class "BdStWeight"
logical vector: indicator which components of z need
to be computed
logical matrix: indicator which components of A need
to be computed
the number of iterations computed so far; used for specifying a different value of the clipping component of the weight in total variation case in the very first iteration.
some IC of class "IC"
further arguments to be passed on E().
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
.checkUpLow checks whether the given clipping height b lies in
\((b_{\rm\scriptstyle min},b_{\rm\scriptstyle min})\);
.getUpperSol determines the upper case/classical solution and computes
corresponding risks
.getLowerSol determines the lower case (minimax bias) solution and computes
corresponding risks
.getLowUpB determines a search interval for b to given radius
r, i.e., lower and upper bounds for
\((b_{\rm\scriptstyle min},b_{\rm\scriptstyle min})\)
.isVirginW checks whether the (total variation) weight w in
the argument has already been modified since creation (TRUE if not)
.checkPIC checks whether (intermediate) results give a pIC
.LowerCaseMultivariatefunction determines the Lagrange multipliers for
the multivariate lower case solution for convex contamination
by solving a corresponding dual problem (Rieder[94],p.199 eq.(18)).
.LowerCaseMultivariatefunctionTV determines the Lagrange multipliers for
the multivariate lower case solution for total variation in dimension \(p=1\)
and \(k>1\) by solving a corresponding dual problem (Rieder[94],p.205 eq.(58)).
.getSB computes the bias and (the square root of the trace of) the variance
of the IC.
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.