SimStudies {RobLoxBioC}

Perform Monte-Carlo Study.

Description

The function AffySimStudy can be used to perform Monte-Carlo studies comparing Tukey's biweight and rmx estimators for normal location and scale. The function IlluminaSimStudy can be used to perform Monte-Carlo studies comparing Illumina's default method - a Huber-type skipped mean and sd (cf. Hampel (1985)) - and rmx estimators for 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

AffySimStudy(n, M, eps, seed = 123, eps.lower = 0, eps.upper = 0.05, 
             steps = 3L, fsCor = TRUE, contD, plot1 = FALSE, 
             plot2 = FALSE, plot3 = FALSE)
IlluminaSimStudy(n, M, eps, seed = 123, eps.lower = 0, eps.upper = 0.05, 
                 steps = 3L, fsCor = TRUE, contD, 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].

seed

random seed.

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.

contD

object of class "UnivariateDistribution"; contaminating distribution.

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.

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 [e-mail]

References

Affymetrix, Inc. (2002). Statistical Algorithms Description Document. Affymetrix, Santa Clara.

Hampel F.R. (1985). The breakdown points of the mean combined with some rejection rules. Technometrics, 27(2):95-107.

See Also

rowRoblox

Examples

set.seed(123) # to have reproducible results for package checking

AffySimStudy(n = 11, M = 100, eps = 0.02, contD = Norm(mean = 0, sd = 3), 
             plot1 = TRUE, plot2 = TRUE, plot3 = TRUE)
IlluminaSimStudy(n = 30, M = 100, eps = 0.02, contD = Norm(mean = 0, sd = 3), 
                 plot1 = TRUE, plot2 = TRUE, plot3 = TRUE)