roblm.whm: Weighted Heteroskedastic M-Regression Estimator
In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description Usage Arguments Value References

This implements Carroll and Rupert's (1982) heteroskedastic M-estimator. It combines M-estimation with the feasible generalized least squares approach, which entails estimating a linear model and utilizing the residuals to construct a covariance matrix of the errors, \widehat{Ω}, to be used in a weighted information matrix, (X^T \hat{Ω}^{-1} X)^{-1} for the generalized least squares step. This is similar to the process of constructing a Huber-White Variance-Covariance matrix for least squares coefficients, except here the estimated error covariance is used to re-estimate the model. Therefore, this method combines the benefits of the feasible GLS approach with the robustness of M-estimation.

The original formulation of this model used Huber's psi function, and a simple Huber M-estimator as the initial step. This is the default here, however, one can also select from the Theil-Sen and Least Absolute Deviations regressions as the initializer. Additional psi functions are also offered including Hampel's psi function, Tukey's bisquare, Yohai & Zamar's optimal psi function, and the power exponential psi function.

roblm.whm(
  formula,
  data,
  varfun = c("power", "exponential"),
  init = c("huber", "theilsen", "lad"),
  psifun = c("optimal", "huber", "bisquare", "hampel", "powexp"),
  maxit = 100,
  control = list(hu.k = 1.345, ha.k = 0.902, bs.c = 4.685, opt.c = 1, pe.c = 1.48, pe.e
    = 1.25)
)

`formula`	model formula
`data`	data frame
`varfun`	the name of the desired heteroskedasic variance function. One of "power" or "exponential".
`init`	the intial algorithm to use. one of "huber" (`roblm`), "theilsen" (`roblm.ts`), or "lad" ((`qreg`) with q=0.50).
`psifun`	one of "optimal", "huber", "bisquare", "hampel", or "powexp"
`maxit`	maximum number of IRWLS iterations. defaults to 100.
`control`	a list of named tuning parameters. they must be named as in the defaults, (hu.k = 1.345, ha.k = 0.902, bs.c = 4.685, opt.c = 1, pe.c = 1.48, pe.e = 1.25; corresponding to "huber", "hampel", "bisquare", "optimal", and "powexp"). however, only the ones relevant to the chosen psi funtion are needed if custom values are desired.the defaults aim to achieve 95 relative efficiency when the residuals are normally distributed with no outliers.