RobLox: showdown – R documentation

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showdown

Estimator Showdown by Monte-Carlo Study.

Description

The function showdown can be used to perform Monte-Carlo studies comparing a competitor with rmx estimators in case of normal location and scale. In addition, maximum likelihood (ML) estimators (mean and sd) and median and MAD are computed. The comparison is based on the empirical MSE.

Usage

showdown(n, M, eps, contD, seed = 123, estfun, estMean, estSd,
         eps.lower = 0, eps.upper = 0.05, steps = 3L, fsCor = TRUE, 
         plot1 = FALSE, plot2 = FALSE, plot3 = FALSE)

Arguments

`n`	integer; sample size, should be at least 3.
`M`	integer; Monte-Carlo replications.
`eps`	amount of contamination in [0, 0.5].
`contD`	object of class `"UnivariateDistribution"`; contaminating distribution.
`seed`	random seed.
`estfun`	function to compute location and scale estimator; see details below.
`estMean`	function to compute location estimator; see details below.
`estSd`	function to compute scale estimator; see details below.
`eps.lower`	used by rmx estimator.
`eps.upper`	used by rmx estimator.
`steps`	integer; steps used for estimator construction.
`fsCor`	logical; use finite-sample correction.
`plot1`	logical; plot cdf of ideal and real distribution.
`plot2`	logical; plot 20 (or M if M < 20) randomly selected samples.
`plot3`	logical; generate boxplots of the results.

Details

Normal location and scale with mean = 0 and sd = 1 is used as ideal model (without restriction due to equivariance).

Since there is no estimator which yields reliable results if 50 percent or more of the observations are contaminated, we use a modification where we re-simulate all samples including at least 50 percent contaminated data.

If estfun is specified it has to compute and return a location and scale estimate (vector of length 2). One can also specify the location and scale estimator separately by using estMean and estSd where estMean computes and returns the location estimate and estSd the scale estimate.

We use funtion rowRoblox for the computation of the rmx estimator.

Value

Data.frame including empirical MSE (standardized by sample size n) and relMSE with respect to the rmx estimator.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

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

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

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

Examples

library(MASS)
## compare with Huber's Proposal 2
showdown(n = 20, M = 100, eps = 0.02, contD = Norm(mean = 3, sd = 3), 
         estfun = function(x){ unlist(hubers(x)) },
         plot1 = TRUE, plot2 = TRUE, plot3 = TRUE)

## compare with Huber M estimator with MAD scale
showdown(n = 20, M = 100, eps = 0.02, contD = Norm(mean = 3, sd = 3), 
         estfun = function(x){ unlist(huber(x)) },
         plot1 = TRUE, plot2 = TRUE, plot3 = TRUE)

RobLox

Optimally Robust Influence Curves and Estimators for Location and Scale

v1.2.0

LGPL-3

Authors

Matthias Kohl [cre, cph], Peter Ruckdeschel [aut, cph]

Initial release

2019-04-02