ridge.bim: Robust Ridge Regression

In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description

This function utilizes an iteratively reweighted and regularized least squares algorithm (IRRWLS) to estimate a robust ridge regression estimator. Robustness weights are estimated in this iterative process using a user-specified weight function (defaults to Yohai & Zamar's optimal psi-function) multiplied by Mallow's weights to yield Schweppe weights: w(ψ) \cdot sqrt(1-h). The ridge penalty λ can be user specified, or left as the default option of using the recommended analytical formula from Kibria and Banik (2016). This obviates the necessity of cross-validation. Data are automatically unit scaled and centered using Yohai and Zou's τ-estimator of location and scale. Coefficients and fitted values are returned on the original scale of the inputs. Hence, it is not neccessary to standardize the inputs.

Usage

ridge.bim(
  formula,
  data,
  psifun = wt.opt,
  lambda = NULL,
  maxit = 100,
  tol = 1e-04,
  ...
)

Arguments

formula	model formula
data	data frame
psifun	function that produces weights from \frac{ψ(u)}{u}. the default is wt.opt.
lambda	the ridge tuning constant. defaults to NULL, in which case an analytical formula from Kibria (2016) is used. See the referenced paper for other potential formulas for use.
maxit	maximum number of iterations for the IRRWLS algorithm.
tol	convergence tolerance. defaults to 1e-4.
...	other arguments to pass to psifun.

Value

a list

References

G. Kibria and S. Banik (2016) Some ridge regression estimators and their performance. Journal of Modern Applied Statistical Methods, 15, 206-238. https://doi.org/10.22237/jmasm/1462075860

abnormally-distributed/cvreg documentation built on May 3, 2020, 3:45 p.m.