lmrob.control: 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 wil

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.

expected value under the normal model of the chi (rather $\rho (rho)$) 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 f

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 $\psi$-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: rll{ 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 rll{ 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. rl{ 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 }

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.

Examples

Run this code

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