getinfLM: Functions to determine Lagrange multipliers
In ROptEst: Optimally Robust Estimation

Description Usage Arguments Value Author(s) References See Also

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.

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, ...)

`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`.

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