lmrobdet.control: Tuning parameters for lmrobdetMM and lmrobdetDCML

Description

This function sets tuning parameters for the MM estimator implemented in lmrobdetMM and the Distance Constrained Maximum Likelihood regression estimators computed by lmrobdetDCML.

Usage

lmrobdet.control(
  bb = 0.5,
  efficiency = 0.95,
  family = "mopt",
  tuning.psi,
  tuning.chi,
  compute.rd = FALSE,
  corr.b = TRUE,
  split.type = "f",
  initial = "S",
  max.it = 100,
  refine.tol = 1e-07,
  rel.tol = 1e-07,
  refine.PY = 10,
  solve.tol = 1e-07,
  trace.lev = 0,
  psc_keep = 0.5,
  resid_keep_method = "threshold",
  resid_keep_thresh = 2,
  resid_keep_prop = 0.2,
  py_maxit = 20,
  py_eps = 1e-05,
  mscale_maxit = 50,
  mscale_tol = 1e-06,
  mscale_rho_fun = "bisquare"
)

Value

A list with the necessary tuning parameters.

Arguments

bb: tuning constant (between 0 and 1/2) for the M-scale used to compute the initial S-estimator. It determines the robusness (breakdown point) of the resulting MM-estimator, which is bb. Defaults to 0.5.
efficiency: desired asymptotic efficiency of the final regression M-estimator. Defaults to 0.95.
family: string specifying the name of the family of loss function to be used (current valid options are "bisquare", "opt" and "mopt"). Incomplete entries will be matched to the current valid options. Defaults to "mopt".
tuning.psi: tuning parameters for the regression M-estimator computed with a rho function as specified with argument family. If missing, it is computed inside lmrobdet.control to match the value of efficiency according to the family of rho functions specified in family. Appropriate values for tuning.psi for a given desired efficiency for Gaussian errors can be constructed using the functions bisquare, mopt and opt.
tuning.chi: tuning constant for the function used to compute the M-scale used for the initial S-estimator. If missing, it is computed inside lmrobdet.control to match the value of bb according to the family of rho functions specified in family.
compute.rd: logical value indicating whether robust leverage distances need to be computed.
corr.b: logical value indicating whether a finite-sample correction should be applied to the M-scale parameter bb.
split.type: determines how categorical and continuous variables are split. See splitFrame.
initial: string specifying the initial value for the M-step of the MM-estimator. Valid options are 'S', for an S-estimator and 'MS' for an M-S estimator which is appropriate when there are categorical explanatory variables in the model.
max.it: maximum number of IRWLS iterations for the MM-estimator
refine.tol: relative covergence tolerance for the S-estimator
rel.tol: relative covergence tolerance for the IRWLS iterations for the MM-estimator
refine.PY: number of refinement steps for the Pen~a-Yohai candidates
solve.tol: (for the S algorithm): relative tolerance for matrix inversion. Hence, this corresponds to solve.default's tol.
trace.lev: positive values (increasingly) provide details on the progress of the MM-algorithm
psc_keep: For pyinit, proportion of observations to remove based on PSCs. The effective proportion of removed observations is adjusted according to the sample size to be prosac*(1-p/n). See pyinit.
resid_keep_method: For pyinit, how to clean the data based on large residuals. If "threshold", all observations with scaled residuals larger than C.res will be removed, if "proportion", observations with the largest prop residuals will be removed. See pyinit.
resid_keep_thresh: See parameter resid_keep_method above. See pyinit.
resid_keep_prop: See parameter resid_keep_method above. See pyinit.
py_maxit: Maximum number of iterations. See pyinit.
py_eps: Relative tolerance for convergence. See pyinit.
mscale_maxit: Maximum number of iterations for the M-scale algorithm. See pyinit and mscale.
mscale_tol: Convergence tolerance for the M-scale algorithm. See mscale and mscale.
mscale_rho_fun: String indicating the loss function used for the M-scale. See pyinit.

Author

Matias Salibian-Barrera, matias@stat.ubc.ca

Details

The argument family specifies the name of the family of loss function to be used. Current valid options are "bisquare", "opt" and "mopt"--"opt" refers to the optimal psi function defined in Section 5.8.1. of the book Robust Statistics: Theory and Methods (with R) by Maronna, Martin, Yohai and Salibian-Barrera, "mopt" is a modified version of the optimal psi function to make it strictly increasing close to 0, and to make the corresponding weight function non-increasing near 0.

Examples

Run this code

data(coleman, package='robustbase')
m2 <- lmrobdetMM(Y ~ ., data=coleman, control=lmrobdet.control(refine.PY=50))
m2
summary(m2)

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