fsRadius: Finite-sample Corrected Radius

In stamats/rmx: Radius-Minimax Estimators

Finite-sample Corrected Radius

Description

Given some radius and some sample size the function computes the corresponding finite-sample corrected radius. The user should use function fsRadius. The other functions are rarely called directly and are mainly for internal use.

Usage

fsRadius(r, n, model = "norm", ...)

fsRadius.norm(r, n)

fsRadius.binom(r, n, prob, size, M = 10000, parallel = FALSE, ncores = NULL)

fsRadius.pois(r, n, lambda, M = 10000, parallel = FALSE, ncores = NULL)

Arguments

r	asymptotic radius (non-negative numeric)
n	sample size
model	character: short name of the model/distribution (default = "norm"); see also details.
prob	prob parameter; see dbinom.
size	size parameter (known!); see dbinom.
lambda	lambda parameter; see dpois.
M	number of Monte-Carlo simulations; see details below.
parallel	logical: use package parallel for computations.
ncores	if parallel = TRUE: number of cores used for computations. If missing, the maximum number of cores - 1 is used.
...	further arguments passed through; e.g., known parameters such as size in case of the binomial model.

Details

The finite-sample correction is based on empirical results obtained via Monte-Carlo simulations.

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 is minimized for the class of optimally robust estimators and the corresponding finite-sample radius determined.

For some models ("norm") the computation is based on the saved results of the Monte-Carlo simulations, whereas for other models ("binom", "pois") the results are computed inside of the function based on M Monte-Carlo simulations.

As models we have implemented so far:

1. "norm": normal location (mean) and scale (sd)

2. "binom": probability of success (prob)

3. "pois": Poisson mean (lambda)

Value

Finite-sample corrected radius.

Author(s)

Matthias Kohl [e-mail]

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

See Also

rmx, rowRmx

Examples

## finite-sample radius is larger (more conservative)
fsRadius(r = 0.5, n = 3, model = "norm")
fsRadius(r = 0.5, n = 10, model = "norm")
fsRadius(r = 0.5, n = 25, model = "norm")
fsRadius(r = 0.5, n = 50, model = "norm")
fsRadius(r = 0.5, n = 100, model = "norm")
fsRadius(r = 0.5, n = 500, model = "norm")
fsRadius(r = 0.5, n = 1000, model = "norm")

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