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

 getInfLM R Documentation

## 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_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 peter.ruckdeschel@uni-oldenburg.de

### 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.

`InfRobModel-class`