internals: Internal / Helper functions of package ROptEst

In ROptEst: Optimally Robust Estimation

Internal / Helper functions of package ROptEst

Description

These functions are used internally by package ROptEst.

Usage

### 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, ...)

Arguments

L2deriv	L2-derivative of some L2-differentiable family of probability measures.
b	numeric; clipping bound under consideration.
risk	object of class "RiskType".
neighbor	object of class "Neighborhood".
biastype	object of class "BiasType" — the bias type with we work.
normtype	object of class "NormType" — the norm type with we work.
Distr	object of class "Distribution".
Finfo	Fisher information matrix.
DistrSymm	object of class "DistributionSymmetry".
L2derivSymm	object of class "FunSymmList".
L2derivDistrSymm	object of class "DistrSymmList".
z.start	initial value for the centering constant.
A.start	initial value for the standardizing matrix.
trafo	matrix: transformation of the parameter.
maxiter	the maximum number of iterations.
tol	the desired accuracy (convergence tolerance).
QuadForm	matrix of (or which may coerced to) class PosSemDefSymmMatrix for use of different (standardizing) norm
verbose	logical: if TRUE, some messages are printed.
nrvalpts	integer: number of evaluation points.
warn	logical: print warnings.
radius	radius of the neighborhood.
z	centering constant (in k-space)
A	standardizing matrix.
w	a weight of class "BdStWeight"
z.comp	logical vector: indicator which components of z need to be computed
A.comp	logical matrix: indicator which components of A need to be computed
iter	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.
IC	some IC of class "IC"
...	further arguments to be passed on E().

Details

.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.

Value

.checkUpLow	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.
.getUpperSol	a return list for getInfRobIC
.getLowerSol	a return list for getInfRobIC
.checkUpLow	a list with items lower and upper (both numeric).
.isVirginW	TRUE or FALSE
.checkPIC	nothing is returned; precision values are issued.
.LowerCaseMultivariatefunction	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.
.LowerCaseMultivariatefunctionTV	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.
.getSB	a list with elements s, (the square root of the trace of) the variance and b, the bias.

Author(s)

Peter Ruckdeschel [e-mail]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

ROptEst documentation built on Feb. 7, 2024, 3:02 p.m.