rlsOptIC.AL {RobLox} | R Documentation |
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).
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)
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. |
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.
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 |
Matthias Kohl Matthias.Kohl@stamats.de
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
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))