rlsOptIC.AL {RobLox}R Documentation

Computation of the optimally robust IC for AL estimators

Description

The function rlsOptIC.AL computes the optimally robust IC for AL estimators in case of normal location with unknown scale and (convex) contamination neighborhoods. The definition of these estimators can be found in Section 8.2 of Kohl (2005).

Usage

rlsOptIC.AL(r, mean = 0, sd = 1, A.loc.start = 1, a.sc.start = 0, 
            A.sc.start = 0.5, bUp = 1000, delta = 1e-6, itmax = 100, 
            check = FALSE, computeIC = TRUE)

Arguments

r non-negative real: neighborhood radius.
mean specified mean.
sd specified standard deviation.
A.loc.start positive real: starting value for the standardizing constant of the location part.
a.sc.start real: starting value for centering constant of the scale part.
A.sc.start positive real: starting value for the standardizing constant of the scale part.
bUp positive real: the upper end point of the interval to be searched for the clipping bound b.
delta the desired accuracy (convergence tolerance).
itmax the maximum number of iterations.
check logical: should constraints be checked.
computeIC logical: should IC be computed. See details below.

Details

The Lagrange multipliers contained in the expression of the optimally robust IC can be accessed via the accessor functions cent, clip and stand. If 'computeIC' is 'FALSE' only the Lagrange multipliers 'A', 'a', and 'b' contained in the optimally robust IC are computed.

Value

If 'computeIC' is 'TRUE' an object of class "ContIC" is returned, otherwise a list of Lagrane multipliers

A standardizing matrix
a centering vector
b optimal clipping bound

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

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

ContIC-class, roblox

Examples

IC1 <- rlsOptIC.AL(r = 0.1, check = TRUE)
distrExOptions("ErelativeTolerance" = 1e-12)
checkIC(IC1)
distrExOptions("ErelativeTolerance" = .Machine$double.eps^0.25) # default
Risks(IC1)
cent(IC1)
clip(IC1)
stand(IC1)
plot(IC1)
infoPlot(IC1)

## one-step estimation
## see also: ?roblox
## 1. data: random sample
ind <- rbinom(100, size=1, prob=0.05) 
x <- rnorm(100, mean=0, sd=(1-ind) + ind*9)
mean(x)
sd(x)
median(x)
mad(x)

## 2. Kolmogorov(-Smirnov) minimum distance estimator
## -> we use it as initial estimate for one-step construction
(est0 <- ksEstimator(x=x, Norm()))

## 3. one-step estimation: radius known
IC1 <- rlsOptIC.AL(r = 0.5, mean = est0$mean, sd = est0$sd)
(est1 <- oneStepEstimator(x, IC1, est0))

## 4. one-step estimation: radius unknown
## take least favorable radius r = 0.579
## cf. Table 8.1 in Kohl(2005)
IC2 <- rlsOptIC.AL(r = 0.579, mean = est0$mean, sd = est0$sd)
(est2 <- oneStepEstimator(x, IC2, est0))

[Package RobLox version 0.5.0 Index]