getinfLM: Functions to determine Lagrange multipliers

Description Usage Arguments Value Author(s) References See Also

Description

Functions to determine Lagrange multipliers A and a in a Hampel problem or in a(n) (inner) loop in a MSE problem; can be done either by optimization or by fixed point iteration. These functions are rarely called directly.

Usage

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getLagrangeMultByIter(b, L2deriv, risk, trafo,
                      neighbor, biastype, normtype, Distr,
                      a.start, z.start, A.start, w.start, std, z.comp,
                      A.comp, maxiter, tol, verbose = NULL,
                      warnit = TRUE, ...)
getLagrangeMultByOptim(b, L2deriv, risk, FI, trafo,
                      neighbor, biastype, normtype, Distr,
                      a.start, z.start, A.start, w.start,  std, z.comp,
                      A.comp, maxiter, tol, verbose = NULL, ...)

Arguments

b

numeric; (>b_min; clipping bound for which the Lagrange multipliers are searched

L2deriv

L2-derivative of some L2-differentiable family of probability measures.

risk

object of class "RiskType".

FI

matrix: Fisher information.

trafo

matrix: transformation of the parameter.

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".

a.start

initial value for the centering constant (in p-space).

z.start

initial value for the centering constant (in k-space).

A.start

initial value for the standardizing matrix.

w.start

initial value for the weight function.

std

matrix of (or which may coerced to) class PosSemDefSymmMatrix for use of different (standardizing) norm.

z.comp

logical vector: indication which components of the centering constant have to be computed.

A.comp

matrix: indication which components of the standardizing matrix have to be computed.

maxiter

the maximum number of iterations.

tol

the desired accuracy (convergence tolerance).

verbose

logical: if TRUE, some messages are printed.

warnit

logical: if TRUE warning is issued if maximal number of iterations is reached.

...

additional parameters for optim and E.

Value

a list with items

A

Lagrange multiplier A (standardizing matrix)

a

Lagrange multiplier a (centering in p-space)

z

Lagrange multiplier z (centering in k-space)

w

weight function involving Lagrange multipliers

biastype

(possibly modified) bias type biastype from argument

normtype

(possibly modified) norm type normtype from argument

normtype.old

(possibly modified) norm type normtype before last (internal) update

risk

(possibly [norm-]modified) risk risk from argument

std

(possibly modified) argument std

iter

number of iterations needed

prec

precision achieved

b

used clippng height b

call

call with which either getLagrangeMultByIter or getLagrangeMultByOptim was called

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106-115.

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

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22: 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

InfRobModel-class


ROptEst documentation built on May 2, 2019, 5:45 p.m.