optIF: Computation of the optimally robust IF for AL estimators

In stamats/rmx: Radius-Minimax Estimators

Computation of the optimally robust IF for AL estimators

Description

The function computes the optimally robust IF for AL estimators in case of shrinking contamination neighborhoods / gross error models. The definition of these estimators can be found in Rieder (1994) and Kohl (2005).

Usage

optIF(model = "norm", radius = NULL, ...)

## S3 method for class 'optIF'
print(x, digits = getOption("digits"), prefix = " ", ...)

## S3 method for class 'optIF'
summary(object, digits = getOption("digits"), prefix = " ", ...)

## S3 method for class 'optIF'
plot(x, alpha = 1e-6, digits = 2, plot = TRUE, n = 501, ...)

Arguments

model	character: short name of the model/distribution (default = "norm"); see also details.
radius	non-negative real: neighborhood radius.
x	an optIF object.
object	an optIF object.
alpha	alpha-quantile used to compute plot range, which is from alpha-quantile to 1-alpha-quantile of the fitted model.
digits	minimal number of significant digits.
prefix	string, passed to strwrap.
plot	logical: generate plot, sometimes usefull to suppress plotting and modify the returned ggplot object.
n	number of points to evaluate the IF in case of continuous models.
...	further arguments passed through sucha as model parameter(s); see details.

Details

The Lagrange multipliers contained in the expression of the optimally robust IF are computed; i.e., clipping constant, centering vector and standardising matrix. For more details we refer to Rieder (1994) or Kohl (2005).

As models we have implemented so far:

1. "norm": normal location (mean) and scale (sd); see also optIF.norm.

2. "binom": binomial probability (size known); see also optIF.binom.

3. "pois": Poisson mean; see also optIF.pois.

4. "exp": Exponential scale; see also optIF.exp.

Value

An object of class "optIF" is returned. It contains at least 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
call	matched call

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

rmx

Examples

## normal location and scale
IF1 <- optIF(model = "norm", radius = 0.5, mean = -2, sd = 3)
IF1
summary(IF1)
plot(IF1)

## binomial probability
IF2 <- optIF(model = "binom", radius = 0.5, size = 10)
IF2
summary(IF2)
plot(IF2)

## Poisson mean
IF3 <- optIF(model = "pois", radius = 0.5)
IF3
summary(IF3)
plot(IF3)

## Exponential scale
IF4 <- optIF(model = "exp", radius = 0.5)
IF4
summary(IF4)
plot(IF4)

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