cniper: Cniper Region

In stamats/rmx: Radius-Minimax Estimators

Cniper Region

Description

The function cniper computes cniper regions by comparing the maximum asymptotic MSE of ML and RMX estimators under contaminations by Dirac point measures.

Usage

cniper(x, ...)

## S3 method for class 'rmx'
cniper(x, range.alpha = 1e-6, ...)

## S3 method for class 'cniper'
print(x, digits = 3, ...)

## S3 method for class 'cniper'
plot(x, add.data = TRUE, color.data = "#0072B5",
                      alpha.data = 0.4, range.alpha = 1e-6, range.n = 501, 
                      color.vline = "#E18727", 
                      ggplot.ggtitle = "Cniper Contamination", 
                      ggplot.xlab = "contamination point", 
                      ggplot.ylab = "asMSE(ML) - asMSE(RMX)", ...)

Arguments

x	object of S3 class rmx.
range.alpha	alpha-quantile used to determine the search region for cniper points.
digits	minimal number of significant digits.
add.data	logical: add data points to the plot.
color.data	character: color used for plotting the data points.
alpha.data	numeric: amount of alpha shading used for plotting the data points.
range.n	numeric: number of points used for plotting the curve of the MSE differences.
color.vline	character: color used for plotting the boundaries of the cniper region.
ggplot.ggtitle	character: title of the plot.
ggplot.xlab	character: label of x-axis.
ggplot.ylab	character: label of y-axis.
...	further arguments passed through.

Details

The function is inspired by the respective functions of the RobASt-family of packages.

In case of optimally-robust RMX estimators computed with function rmx (S3 class rmx), cniper regions are computed by comparing the maximum asymptotic MSE of the RMX estimator with the maximum asyptotic MSE of the ML estimator. For more details about the cniper concept we refer to the Introduction of Kohl (2005) and Section 5 of Ruckdeschel (2010).

Value

An object of class "cniper" is returned. It contails at least the following arguments:

rmx	object of class rmx.
lower	lower boundary of cniper region.
upper	upper boundary of cniper region.
prop.cniper	proportion of data in the cniper region.
p.cniper	probability of the cniper region under the fitted model.
prop.lower	proportion of data in the lower cniper region.
prop.upper	proportion of data in the upper cniper region.
p.lower	probability of the lower cniper region under the fitted model.
p.upper	probability of the upper cniper region under the fitted model.

Author(s)

Matthias Kohl [e-mail]

References

Kohl, M. (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

M. Kohl, P. Ruckdeschel, and H. Rieder (2010). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Statistical Methods and Application, 19(3):333-354.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications 17(1) 13-40. Extended version: http://r-kurs.de/RRlong.pdf.

Ruckdeschel, P. (2010). Consequences of Higher Order Asymptotics for the MSE of M-estimators on Neighborhoods. arXiv, https://arxiv.org/abs/1006.0123.

See Also

rmx, getCnipers, outlier

Examples

ind <- rbinom(100, size=1, prob=0.05) 
x <- rnorm(100, mean=ind*3, sd=(1-ind) + ind*9)
res <- rmx(x, eps.lower = 0.01, eps.upper = 0.1)
(cni.res <- cniper(res))
plot(cni.res)

stamats/rmx documentation built on Sept. 29, 2023, 7:13 p.m.