roblox {RobLox}R Documentation

Optimally robust estimator for location and/or scale

Description

The function roblox computes the optimally robust estimator and corresponding IC for normal location und/or scale and (convex) contamination neighborhoods. The definition of these estimators can be found in Rieder (1994) or Kohl (2005), respectively.

Usage

roblox(x, mean, sd, eps, eps.lower, eps.upper, initial.est, k = 1, returnIC = FALSE)

Arguments

x vector x of data values, may also be a matrix or data.frame with one row, respectively one column/(numeric) variable.
mean specified mean.
sd specified standard deviation which has to be positive.
eps positive real (0 < eps <= 0.5): amount of gross errors. See details below.
eps.lower positive real (0 <= eps.lower <= eps.upper): lower bound for the amount of gross errors. See details below.
eps.upper positive real (eps.lower <= eps.upper <= 0.5): upper bound for the amount of gross errors. See details below.
initial.est initial estimate for mean and/or sd. If missing median and/or MAD are used.
k positive integer. k-step is used to compute the optimally robust estimator.
returnIC logical: should IC be returned. See details below.

Details

Computes the optimally robust estimator for location with scale specified, scale with location specified, or both if neither is specified. The computation uses a k-step construction with an appropriate initial estimate for location or scale or location and scale, respectively. Valid candidates are e.g. median and/or MAD (default) as well as Kolmogorov(-Smirnov) or von Mises minimum distance estimators; cf. Rieder (1994) and Kohl (2005).

If the amount of gross errors (contamination) is known, it can be specified by eps. The radius of the corresponding infinitesimal contamination neighborhood is obtained by multiplying eps by the square root of the sample size.

If the amount of gross errors (contamination) is unknown, try to find a rough estimate for the amount of gross errors, such that it lies between eps.lower and eps.upper.

In case eps.lower is specified and eps.upper is missing, eps.upper is set to 0.5. In case eps.upper is specified and eps.lower is missing, eps.lower is set to 0.

If neither eps nor eps.lower and/or eps.upper is specified, eps.lower and eps.upper are set to 0 and 0.5, respectively.

If eps is missing, the radius-minimax estimator in sense of Rieder et al. (2001, 2008), respectively Section 2.2 of Kohl (2005) is returned.

Value

Object of class "kStepEstimate".

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.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not Knowing the Radius. Submitted. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under www.uni-bayreuth.de/departments/math/org/mathe7/RIEDER/pubs/RR.pdf

See Also

ContIC-class, rlOptIC, rsOptIC, rlsOptIC.AL, kStepEstimate-class, roptest

Examples

ind <- rbinom(100, size=1, prob=0.05) 
x <- rnorm(100, mean=ind*3, sd=(1-ind) + ind*9)

## amount of gross errors known
res1 <- roblox(x, eps = 0.05, returnIC = TRUE)
estimate(res1)
pIC(res1)
checkIC(pIC(res1))
Risks(pIC(res1))
Infos(pIC(res1))
plot(pIC(res1))
infoPlot(pIC(res1))

## amount of gross errors unknown
res2 <- roblox(x, eps.lower = 0.01, eps.upper = 0.1, returnIC = TRUE)
estimate(res2)
pIC(res2)
checkIC(pIC(res2))
Risks(pIC(res2))
Infos(pIC(res2))
plot(pIC(res2))
infoPlot(pIC(res2))

## estimator comparison
# classical optimal (non-robust)
c(mean(x), sd(x))

# most robust
c(median(x), mad(x))

# optimally robust (amount of gross errors known)
estimate(res1)

# optimally robust (amount of gross errors unknown)
estimate(res2)

# Kolmogorov(-Smirnov) minimum distance estimator (robust)
(ks.est <- MDEstimator(x, ParamFamily = NormLocationScaleFamily()))

# optimally robust (amount of gross errors known)
roblox(x, eps = 0.05, initial.est = estimate(ks.est))

# Cramer von Mises minimum distance estimator (robust)
(CvM.est <- MDEstimator(x, ParamFamily = NormLocationScaleFamily(), distance = CvMDist))

# optimally robust (amount of gross errors known)
roblox(x, eps = 0.05, initial.est = estimate(CvM.est))

[Package RobLox version 0.6.1 Index]