getinfLM: Functions to determine Lagrange multipliers

In ROptEst: Optimally Robust Estimation

Functions to determine Lagrange multipliers

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

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_{\rm\scriptstyle 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 [e-mail]

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 Sept. 12, 2024, 7:40 a.m.