cniperCont: Functions for Computation and Plot of Cniper Contamination...

In ROptEst: Optimally Robust Estimation

Functions for Computation and Plot of Cniper Contamination and Cniper Points.

Description

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.

Usage

cniperCont(IC1, IC2, data = NULL, ...,
           neighbor, risk, lower=getdistrOption("DistrResolution"),
           upper=1-getdistrOption("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=1-getdistrOption("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)

Arguments

IC1	object of class IC
IC2	object of class IC
L2Fam	object of class L2ParamFamily
neighbor	object of class Neighborhood
risk	object of class RiskType
...	additional parameters (in particular to be passed on to plot).
data	data to be plotted in
lower, upper	the lower and upper end points of the contamination interval (in prob-scale).
n	number of points between lower and upper
withMaxRisk	logical; if TRUE, for risk comparison uses the maximal risk of the classically optimal IC \psi in all situations with contamination in Dirac points 'no larger' than the respective evaluation point and the optimally-robust IC \eta at its least favorable contamination situation ('over all real Dirac contamination points'). This is the default and was the behavior prior to package version 0.9). If FALSE it uses exactly the situation with Dirac contamination in the evaluation point for both ICs \psi and \eta which amounts to calling cniperCont with IC1=psi, IC2=eta.
with.automatic.grid	logical; should a grid be plotted alongside with the ticks of the axes, automatically? If TRUE a respective call to grid in argument panel.first is ignored.
scaleX	logical; shall X-axis be rescaled (by default according to the cdf of the underlying distribution)?
scaleY	logical; shall Y-axis 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 is TRUE and scaleX.fct is missing, the cdf of the underlying observation distribution.
scaleX.inv	the inverse function to scale.fct, i.e., an isotone, vectorized function mapping [0,1] to the domain of the IC(s) such that for any x in the domain, scaleX.inv(scaleX.fct(x))==x; if scaleX is TRUE and scaleX.inv is missing, the quantile function of the underlying observation distribution.
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 {\cal 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 {\cal 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 non-NULL, user-given x-ticks (on original scale);
y.ticks	numeric; defaults to NULL; (then ticks are chosen automatically); if non-NULL, user-given y-ticks (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 NULL (default), then log(1+abs(x)) is used for the rescaling, or a function which is then used for the rescaling.
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 non-labelled points of the data argument plotted (vectorized);
pch.npts	symbol of the non-labelled points of the data argument plotted (vectorized);
cex.npts	size of the non-labelled points of the data argument plotted (vectorized);
cex.npts.fun	rescaling function for the size of the non-labelled points to be plotted; either NULL (default), then log(1+abs(x)) is used for each of the rescalings, or a function which is then used for each of the rescalings.
with.lab	logical; shall labels be plotted to the observations?
lab.pts	character or NULL; labels to be plotted to the observations; if NULL observation indices;
lab.font	font to be used for labels
alpha.trsp	alpha transparency to be added ex post to colors col.pch and col.lbl; if one-dim and NA all colors are left unchanged. Otherwise, with usual recycling rules alpha.trsp gets shorted/prolongated to length the data-symbols to be plotted. Coordinates of this vector alpha.trsp with NA are left unchanged, while for the remaining ones, the alpha channel in rgb space is set to the respective coordinate value of alpha.trsp. The non-NA entries must be integers in [0,255] (0 invisible, 255 opaque).
jit.fac	jittering factor used in case of a DiscreteDistribution for plotting points of the second argument in a jittered fashion.
jit.tol	jittering tolerance used in case of a DiscreteDistribution for plotting points of the second argument in a jittered fashion.
which.lbs	either an integer vector with the indices of the observations to be plotted into graph or NULL — then no observation is excluded
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 NULL — then all non-labelled observations are plotted.
which.Order	we order the observations (descending) according to the norm given by normtype(object); then which.Order either is an integer vector with the indices of the ordered observations (remaining after a possible reduction by argument which.lbs) to be plotted into graph or NULL — then no (further) observation is excluded.
attr.pre	logical; do graphical attributes for plotted data refer to indices prior (TRUE) or posterior to selection via arguments which.lbs, which.Order, which.nonlbs (FALSE)?
return.Order	logical; if TRUE, an order vector is returned; more specifically, the order of the (remaining) observations given by their original index is returned (remaining means: after a possible reduction by argument which.lbs, and ordering is according to the norm given by normtype(object)); otherwise we return invisible() as usual.
withSubst	logical; if TRUE (default) pattern substitution for titles and lables is used; otherwise no substitution is used.
withMakeIC	logical; if TRUE the [p]IC is passed through makeIC before return.

Details

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/date-string 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).

Value

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.

Author(s)

Matthias Kohl [e-mail]

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

M. Kohl, P. Ruckdeschel, and H. Rieder (2010). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Statistical Methods and Applications 19(3): 333-354. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10260-010-0133-0")}.

P. Ruckdeschel (2004). Higher Order Asymptotics for the MSE of M-Estimators on Shrinking Neighborhoods. Unpublished Manuscript.

Examples

## 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)

ROptEst documentation built on Sept. 12, 2024, 7:40 a.m.