lmrob.control {robustbase}R Documentation

Tuning parameters for lmrob

Description

Tuning parameters for lmrob, the MM-type regression estimator and the associated S-, M- and D-estimators. Using setting="KS2011" sets the defaults as suggested by Koller and Stahel (2011).

Usage

lmrob.control(setting, seed = NULL, nResample = 500,
              tuning.chi = NULL, bb = 0.5, tuning.psi = NULL,
              max.it = 50, groups = 5, n.group = 400,
              k.fast.s = 1, best.r.s = 2, k.max = 200,
              refine.tol = 1e-7, rel.tol = 1e-7, trace.lev = 0,
              compute.rd = FALSE, method = 'MM',
              psi = c('bisquare', 'lqq', 'welsh', 'optimal', 'hampel',
              'ggw'), numpoints = 10, cov = '.vcov.avar1', ...)

Arguments

setting

a string specifying alternative default values. Leave empty for the defaults or use KS2011 for the defaults suggested by Koller and Stahel (2011). See Details.

seed

an integer vector, the seed to be used for random re-sampling used in obtaining candidates for the initial S-estimator; see .Random.seed. The current value of .Random.seed will be preserved if seed is set; otherwise (by default), .Random.seed will be modified as usual from calls to runif().

nResample

number of re-sampling candidates to be used to find the initial S-estimator. Currently defaults to 500 which works well in most situations (see references).

tuning.chi

tuning constant vector for the S-estimator. Sensible defaults are set according to psi to yield a 50% breakdown estimator. See Details.

bb

expected value under the normal model of the “chi” (rather rho) function with tuning constant equal to tuning.chi. This is used to compute the S-estimator.

tuning.psi

tuning constant vector for the re-descending M-estimator. Depending on the value of psi this constant is set to yield an estimator with asymptotic efficiency of 95% for normal errors. See Details.

max.it

integer specifying the maximum number of IRWLS iterations.

groups

(for the fast-S algorithm): Number of random subsets to use when the data set is large.

n.group

(for the fast-S algorithm): Size of each of the groups above. Note that this must be at least p.

k.fast.s

(for the fast-S algorithm): Number of local improvement steps (“I-steps”) for each re-sampling candidate.

best.r.s

(for the fast-S algorithm): Number of of best candidates to be iterated further (i.e., “refined”); is denoted t in Salibian-Barrera \& Yohai(2006).

k.max

(for the fast-S algorithm): maximal number of refinement steps for the “fully” iterated best candidates.

refine.tol

(for the fast-S algorithm): relative convergence tolerance for the fully iterated best candidates.

rel.tol

(for the RWLS iterations of the MM algorithm): relative convergence tolerance for the parameter vector.

trace.lev

integer indicating if the progress of the MM-algorithm should be traced (increasingly); default trace.lev = 0 does no tracing.

compute.rd

logical indicating if robust distances (based on the MCD robust covariance estimator covMcd) are to be computed for the robust diagnostic plots. This may take some time to finish, particularly for large data sets, and can lead to singularity problems when there are factor explanatory variables (with many levels, or levels with “few” observations). Hence, is FALSE by default.

method

string specifying the estimator-chain. MM is interpreted as SM. See Details of lmrob for a description of the possible values.

psi

string specifying the type ψ-function used. See Details of lmrob. Defaults to bisquare for S and MM-estimates, otherwise lqq.

numpoints

Number of points used in Gauss quadrature.

cov

Function or string with function name to be used to calculate covariance matrix estimate. See Details of lmrob.

...

Further arguments are added to the control list.

Details

The option setting="KS2011" alters the default arguments. They are changed to method = 'SMDM', psi = 'lqq', max.it = 500, k.max = 2000, cov = '.vcov.w'. The defaults of all the remaining arguments are not changed.

By default, tuning.chi and tuning.psi are set to yield an MM-estimate with break-down point 0.5 and efficiency of 95\% at the normal. They are:

psi tuning.chi tuning.psi
bisquare 1.54764 4.685061
welsh 0.5773502 2.11
ggw c(-0.5, 1.5, NA, 0.5) c(-0.5, 1.5, 0.95, NA)
lqq c(-0.5, 1.5, NA, 0.5) c(-0.5, 1.5, 0.95, NA)
optimal 0.4047 1.060158
hampel c(1.5, 3.5, 8)*0.2119163 c(1.5, 3.5, 8)*0.9014

The values for the tuning constant for the ggw psi function are hard coded. The constants vector has four elements: minimal slope, b (controlling the bend at the maximum of the curve), efficiency, break-down point. Use NA for an unspecified value, see examples in the tables.

The constants for the hampel psi function are chosen to have a redescending slope of -1/3. Constants for a slope of -1/2 would be

psi tuning.chi tuning.psi
hampel c(2, 4, 8)*0.1981319 c(2, 4, 8)*0.690794

Alternative coefficients for an efficiency of 85\% at the normal are given in the table below.

psi tuning.psi
bisquare 3.443689
welsh 1.456
ggw c(-0.5, 1.5, 0.85, NA)
optimal 0.8684
hampel (-1/3) c(1.5, 3.5, 8)*0.5704545
hampel (-1/2) c(2, 4, 8)*0.4769578

Author(s)

Matias Salibian-Barrera, Martin Maechler and Manuel Koller

References

Koller, M. and Stahel, W.A. (2011), Sharpening Wald-type inference in robust regression for small samples, Computational Statistics & Data Analysis 55(8), 2504–2515.

See Also

lmrob, also for references and examples.

Examples

## Show the default settings:
str(lmrob.control())

[Package robustbase version 0.8-0 Index]