finiteSampleCorrection: Function to compute finite-sample corrected radii
Description
Given some radius and some sample size the function computes
the corresponding finite-sample corrected radius.
Usage
finiteSampleCorrection(r, n, model = "locsc")
Arguments
r
asymptotic radius (non-negative numeric)
n
sample size
model
has to be "locsc" (for location and scale),
"loc" (for location) or "sc" (for scale), respectively.
Value
Finite-sample corrected radius.
concept
normal location
normal scale
normal location and scale
finite-sample correction
Details
The finite-sample correction is based on empirical results obtained via
simulation studies.
Given some radius of a shrinking contamination neighborhood which leads
to an asymptotically optimal robust estimator, the finite-sample empirical
MSE based on contaminated samples was minimized for this class of
asymptotically optimal estimators and the corresponding finite-sample
radius determined and saved.
The computation is based on the saved results of these Monte-Carlo simulations.
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://www.stamats.de/RRlong.pdf
finiteSampleCorrection(n = 3, r = 0.001, model = "locsc")
finiteSampleCorrection(n = 10, r = 0.02, model = "loc")
finiteSampleCorrection(n = 250, r = 0.15, model = "sc")