optRisk: Generic function for the computation of the minimal risk

Description Usage Arguments Details Value Methods Author(s) References See Also Examples

Description

Generic function for the computation of the optimal (i.e., minimal) risk for a probability model.

Usage

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
optRisk(model, risk, ...)

## S4 method for signature 'L2ParamFamily,asCov'
optRisk(model, risk)

## S4 method for signature 'InfRobModel,asRisk'
optRisk(model, risk, z.start = NULL,
                   A.start = NULL, upper = 1e4, maxiter = 50,
                   tol = .Machine$double.eps^0.4, warn = TRUE, noLow = FALSE)

## S4 method for signature 'FixRobModel,fiUnOvShoot'
optRisk(model, risk, sampleSize,
                   upper = 1e4, maxiter = 50, tol = .Machine$double.eps^0.4,
                   warn = TRUE, Algo = "A", cont = "left")

Arguments

model

probability model

risk

object of class RiskType

...

additional parameters

z.start

initial value for the centering constant.

A.start

initial value for the standardizing matrix.

upper

upper bound for the optimal clipping bound.

maxiter

the maximum number of iterations

tol

the desired accuracy (convergence tolerance).

warn

logical: print warnings.

sampleSize

integer: sample size.

Algo

"A" or "B".

cont

"left" or "right".

noLow

logical: is lower case to be computed?

Details

In case of the finite-sample risk "fiUnOvShoot" one can choose between two algorithms for the computation of this risk where the least favorable contamination is assumed to be left or right of some bound. For more details we refer to Section 11.3 of Kohl (2005).

Value

The minimal risk is computed.

Methods

model = "L2ParamFamily", risk = "asCov"

asymptotic covariance of L2 differentiable parameteric family.

model = "InfRobModel", risk = "asRisk"

asymptotic risk of a infinitesimal robust model.

model = "FixRobModel", risk = "fiUnOvShoot"

finite-sample under-/overshoot risk of a robust model with fixed neighborhood.

Author(s)

Matthias Kohl [email protected]

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

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

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

See Also

RiskType-class

Examples

1
optRisk(model = NormLocationScaleFamily(), risk = asCov())

ROptEst documentation built on May 31, 2017, 2:50 a.m.