Generic function for the computation of the optimal (i.e., minimal) risk for a probability model.
optRisk(model, risk, ...)# S4 method for L2ParamFamily,asCov
optRisk(model, risk)
# S4 method for InfRobModel,asRisk
optRisk(model, risk, z.start = NULL,
A.start = NULL, upper = 1e4, maxiter = 50,
tol = .Machine$double.eps^0.4, warn = TRUE, noLow = FALSE)
# S4 method for FixRobModel,fiUnOvShoot
optRisk(model, risk, sampleSize,
upper = 1e4, maxiter = 50, tol = .Machine$double.eps^0.4,
warn = TRUE, Algo = "A", cont = "left")
The minimal risk is computed.
probability model
object of class RiskType
additional parameters
initial value for the centering constant.
initial value for the standardizing matrix.
upper bound for the optimal clipping bound.
the maximum number of iterations
the desired accuracy (convergence tolerance).
logical: print warnings.
integer: sample size.
"A" or "B".
"left" or "right".
logical: is lower case to be computed?
asymptotic covariance of L2 differentiable parameteric family.
asymptotic risk of a infinitesimal robust model.
finite-sample under-/overshoot risk of a robust model with fixed neighborhood.
Matthias Kohl Matthias.Kohl@stamats.de
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).
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.
RiskType-class
optRisk(model = NormLocationScaleFamily(), risk = asCov())
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