optIFnorm: Computation of Optimally Robust IFs for Normal Location and...

In stamats/rmx: Radius-Minimax Estimators

Computation of Optimally Robust IFs for Normal Location and Scale

Description

The function computes the optimally robust IF for normal location (mean) and scale (sd). The function is rarely called directly, but via function optIF and is mainly for internal use.

Usage

optIF.norm(radius, mean = 0, sd = 1, A.loc.start = 1, A.sc.start = 0.5, 
           a.sc.start = 0, bUp = 1000, delta = 1e-6, itmax = 100L)

Arguments

radius	non-negative real: neighborhood radius.
mean	mean parameter; see dnorm.
sd	sd parameter; see dnorm.
A.loc.start	numeric: initial value for location component of standardising matrix A.
A.sc.start	numeric: initial value for scale component of standardising matrix A.
a.sc.start	numeric: initial value for scale component of centering vector a.
bUp	postive real: upper limit for clipping constant b.
delta	positive real: desired accuracy (convergence tolerance).
itmax	positive ingeger: maximum number of iterations.

Details

The Lagrange multipliers contained in the expression of the optimally robust IF are computed; i.e., clipping constant, centering vector and standardising matrix; see Chapter 8 of Kohl (2005).

Value

An object of class "optIF" is returned. It contains the following arguments:

model	short name of the model / distribution
modelName	full name of the model
parameter	parameter values of the model
A	standardizing matrix
a	centering vector
b	clipping constant
IFun	influence function
range	function to generate grid for evaluating IFun
asMSE	maximum asymptotic mean squared error (MSE)
asVar	asymptotic (co)variance
asBias	maximum asymptotic bias
radius	neighborhood radius

Author(s)

Matthias Kohl [e-mail]

References

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

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

See Also

optIF

Examples

## IF of ML estimator
optIF.norm(radius = 0)
## IF of MB estimator
optIF.norm(radius = Inf)
## IF of optimally robust AL estimator
optIF.norm(radius = 0.5)

stamats/rmx documentation built on Sept. 29, 2023, 7:13 p.m.