refine.sm {RobStatTM}

IRWLS iterations for S- or M-estimators

Description

This function performs iterative improvements for S- or M-estimators.

Usage

refine.sm(
  x,
  y,
  initial.beta,
  initial.scale,
  k = 50,
  conv = 1,
  b,
  cc,
  family,
  step = "M",
  tol
)

Arguments

x

design matrix

y

vector of responses

initial.beta

vector of initial regression estimates

initial.scale

initial residual scale estimate. If missing the (scaled) median of the absolute residuals is used.

k

maximum number of refining steps to be performed

conv

an integer indicating whether to check for convergence (1) at each step, or to force running k steps (0)

b

tuning constant for the M-scale estimator, used if iterations are for an S-estimator.

cc

tuning constant for the rho function.

family

string specifying the name of the family of loss function to be used (current valid options are "bisquare", "opt" and "mopt")

step

a string indicating whether the iterations are to compute an S-estimator ('S') or an M-estimator ('M')

tol

tolerance to detect convergence (relative difference of consecutive vectors of parameters)

Details

This function performs iterative improvements for S- or M-estimators. Both iterations are formally the same, the only difference is that for M-iterations the residual scale estimate remains fixed, while for S-iterations it is updated at each step. In this case, we follow the Fast-S algorithm of Salibian-Barrera and Yohai an use one step updates for the M-scale, as opposed to a full computation. This as internal function.

Value

A list with the following components:

beta.rw

The updated vector of regression coefficients

scale.rw

The corresponding estimated residual scale

converged

A logical value indicating whether the algorithm converged

Author(s)

Matias Salibian-Barrera, [e-mail].