Description Usage Arguments Details Value Author(s) References Examples
These functions and their methods can be used to determine cniper contamination as well as cniper points. That is, under which (Dirac) contamination is the risk of one procedure larger than the risk of some other procedure.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  cniperCont(IC1, IC2, data = NULL, ...,
neighbor, risk, lower=getdistrOption("DistrResolution"),
upper=1getdistrOption("DistrResolution"), n = 101,
with.automatic.grid = TRUE, scaleX = FALSE, scaleX.fct,
scaleX.inv, scaleY = FALSE, scaleY.fct = pnorm, scaleY.inv=qnorm,
scaleN = 9, x.ticks = NULL, y.ticks = NULL, cex.pts = 1,
cex.pts.fun = NULL, col.pts = par("col"), pch.pts = 19,
cex.npts = 0.6, cex.npts.fun = NULL, col.npts = "red", pch.npts = 20,
jit.fac = 1, jit.tol = .Machine$double.eps, with.lab = FALSE,
lab.pts = NULL, lab.font = NULL, alpha.trsp = NA, which.lbs = NULL,
which.Order = NULL, which.nonlbs = NULL, attr.pre = FALSE,
return.Order = FALSE, withSubst = TRUE)
cniperPoint(L2Fam, neighbor, risk, lower, upper)
cniperPointPlot(L2Fam, data=NULL, ..., neighbor, risk= asMSE(),
lower=getdistrOption("DistrResolution"),
upper=1getdistrOption("DistrResolution"), n = 101,
withMaxRisk = TRUE, with.automatic.grid = TRUE,
scaleX = FALSE, scaleX.fct, scaleX.inv,
scaleY = FALSE, scaleY.fct = pnorm, scaleY.inv=qnorm,
scaleN = 9, x.ticks = NULL, y.ticks = NULL,
cex.pts = 1, cex.pts.fun = NULL, col.pts = par("col"),
pch.pts = 19,
cex.npts = 1, cex.npts.fun = NULL, col.npts = par("col"),
pch.npts = 19,
jit.fac = 1, jit.tol = .Machine$double.eps,
with.lab = FALSE,
lab.pts = NULL, lab.font = NULL, alpha.trsp = NA,
which.lbs = NULL, which.nonlbs = NULL,
which.Order = NULL, attr.pre = FALSE, return.Order = FALSE,
withSubst = TRUE, withMakeIC = FALSE)

IC1 
object of class 
IC2 
object of class 
L2Fam 
object of class 
neighbor 
object of class 
risk 
object of class 
... 
additional parameters (in particular to be passed on to 
data 
data to be plotted in 
lower, upper 
the lower and upper end points of the contamination interval (in probscale). 
n 
number of points between 
withMaxRisk 
logical; if 
with.automatic.grid 
logical; should a grid be plotted alongside
with the ticks of the axes, automatically? If 
scaleX 
logical; shall Xaxis be rescaled (by default according to the cdf of the underlying distribution)? 
scaleY 
logical; shall Yaxis be rescaled (by default according to a probit scale)? 
scaleX.fct 
an isotone, vectorized function mapping the domain of the IC(s)
to [0,1]; if 
scaleX.inv 
the inverse function to 
scaleY.fct 
an isotone, vectorized function mapping for each coordinate the range of the respective coordinate of the IC(s) to [0,1]; defaulting to the cdf of N(0,1). 
scaleY.inv 
an isotone, vectorized function mapping for each coordinate the range [0,1] into the range of the respective coordinate of the IC(s); defaulting to the quantile function of N(0,1). 
scaleN 
integer; defaults to 9; on rescaled axes, number of x and y ticks if drawn automatically; 
x.ticks 
numeric; defaults to NULL; (then ticks are chosen automatically); if nonNULL, usergiven xticks (on original scale); 
y.ticks 
numeric; defaults to NULL; (then ticks are chosen automatically); if nonNULL, usergiven yticks (on original scale); 
cex.pts 
size of the points of the second argument plotted (vectorized); 
cex.pts.fun 
rescaling function for the size of the points to be plotted;
either 
col.pts 
color of the points of the second argument plotted (vectorized); 
pch.pts 
symbol of the points of the second argument plotted (vectorized); 
col.npts 
color of the nonlabelled points of the 
pch.npts 
symbol of the nonlabelled points of the 
cex.npts 
size of the nonlabelled points of the 
cex.npts.fun 
rescaling function for the size of the nonlabelled points
to be plotted; either 
with.lab 
logical; shall labels be plotted to the observations? 
lab.pts 
character or NULL; labels to be plotted to the observations; if 
lab.font 
font to be used for labels 
alpha.trsp 
alpha transparency to be added ex post to colors

jit.fac 
jittering factor used in case of a 
jit.tol 
jittering tolerance used in case of a 
which.lbs 
either an integer vector with the indices of the observations
to be plotted into graph or 
which.nonlbs 
indices of the observations which should be plotted but
not labelled; either an integer vector with the indices of the observations
to be plotted into graph or 
which.Order 
we order the observations (descending) according to the norm given by

attr.pre 
logical; do graphical attributes for plotted data refer
to indices prior ( 
return.Order 
logical; if 
withSubst 
logical; if 
withMakeIC 
logical; if 
In case of cniperCont
the difference between the risks of two ICs
is plotted.
The function cniperPoint
can be used to determine cniper
points. That is, points such that the optimally robust estimator
has smaller minimax risk than the classical optimal estimator under
contamination with Dirac measures at the cniper points.
As such points might be difficult to find, we provide the
function cniperPointPlot
which can be used to obtain a plot
of the risk difference; in this function the usual arguments for
plot
can be used. For arguments col
, lwd
,
vectors can be used; then the first coordinate is taken for the
curve, the second one for the balancing line. For argument lty
,
a list can be used; its first component is then taken for the
curve, the second one for the balancing line.
If argument withSubst
is TRUE
, in all title
and axis lable arguments of cniperCont
and cniperPointPlot
,
the following patterns are substituted:
"%C"
class of argument L2Fam
(for cniperPointPlot
)
"%A"
deparsed argument L2Fam
(for cniperPointPlot
)
"%C1"
class of argument IC1
(for cniperCont
)
"%A1"
deparsed argument IC1
(for cniperCont
)
"%C2"
class of argument IC2
(for cniperCont
)
"%A2"
deparsed argument IC2
(for cniperCont
)
"%D"
time/datestring when the plot was generated
For more details about cniper contamination and cniper points we refer to Section~3.5 of Kohl et al. (2008) as well as Ruckdeschel (2004) and the Introduction of Kohl (2005).
The cniper point is returned by cniperPoint
.
In case of cniperPointPlot
, we return
an S3 object of class c("plotInfo","DiagnInfo")
, i.e., a list
containing the information needed to produce the
respective plot, which at a later stage could be used by different
graphic engines (like, e.g. ggplot
) to produce the plot
in a different framework. A more detailed description will follow in
a subsequent version.
Matthias Kohl [email protected]
Kohl, M. and Ruckdeschel, H. and Rieder, H. (2008). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Unpublished Manuscript.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
Ruckdeschel, P. (2004). Higher Order Asymptotics for the MSE of MEstimators on Shrinking Neighborhoods. Unpublished Manuscript.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  ## cniper contamination
P < PoisFamily(lambda = 4)
RobP1 < InfRobModel(center = P, neighbor = ContNeighborhood(radius = 0.1))
IC1 < optIC(model=RobP1, risk=asMSE())
RobP2 < InfRobModel(center = P, neighbor = ContNeighborhood(radius = 1))
IC2 < optIC(model=RobP2, risk=asMSE())
cniperCont(IC1 = IC1, IC2 = IC2,
neighbor = ContNeighborhood(radius = 0.5),
risk = asMSE(),
lower = 0, upper = 8, n = 101)
## cniper point plot
cniperPointPlot(P, neighbor = ContNeighborhood(radius = 0.5),
risk = asMSE(), lower = 0, upper = 10)
## Don't run to reduce check time on CRAN
## cniper point
cniperPoint(P, neighbor = ContNeighborhood(radius = 0.5),
risk = asMSE(), lower = 0, upper = 4)
cniperPoint(P, neighbor = ContNeighborhood(radius = 0.5),
risk = asMSE(), lower = 4, upper = 8)

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