rliu.rob: Robust Liu's Modified Ridge Estimator

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

Description

The Liu estimator is an augmented version of the ridge estimator. It combines the ridge penalty with a Stein-type penalty. This robust variant uses an S-estimator as the initial starting point for an M-estimator, which is penalized using Liu's method as described in Ertas et al (2017).

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). Likewise with the second penalty term δ, if left as NULL it will automatically be computed using the analytical formula from Alheety and Kibria (2009). The use of analytical formulas obviates the necessity of cross-validation for choosing values or tuning parameters. 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 center and/or standardize the inputs here.

Usage

rliu.rob(
  formula,
  data,
  delta = NULL,
  lambda = NULL,
  psifun = wt.Huber,
  maxit = 100,
  tol = 1e-04,
  ...
)

Arguments

formula	a model formula
data	data frame
delta	the stein penalty, can be user specified, or left as the default option of using the analytical formula from Alheety and Kibria (2009)
lambda	the ridge penalty, can be user specified, or left as the default option of using the recommended analytical formula from Kibria and Banik (2016).
psifun	function that produces weights from \frac{ψ(u)}{u}. the default is wt.Huber.
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

Liu, K. (1993). A new class of biased estimate in linear regression. Communications in Statistics Theory and Methods 22:393–402.

Liu, K. (2003). Using Liu-type estimator to combat collinearity. Communications in Statistics Theory and Methods 32(5):1009–1020.

Alheety, M. I. & Kibria, G. (2009) On the Liu and almost unbiased Liu estimators in the presence of multicollinearity with heteroscedastic or correlated errors. Surveys in Mathematics and its Applications 4:155–167.

Kan, B., Alpu, O. & Yazici, B. (2013) Robust ridge and robust Liu estimator for regression based on the LTS estimator, Journal of Applied Statistics, 40:3, 644-655, DOI: 10.1080/02664763.2012.750285

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

Ertas, H., Kaciranlar, S., & Guer, H. (2017). Robust Liu-type estimator for regression based on M-estimator. Communications in Statistics–Simulation and Computation, 46(5):3907-3932. doi: 10.1080/03610918.2015.1045077

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