optRisk: Generic function for the computation of the minimal risk

In ROptEst: Optimally Robust Estimation

Generic function for the computation of the minimal risk

Description

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

Usage

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 [e-mail]

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

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

ROptEst documentation built on Feb. 7, 2024, 3:02 p.m.