robpr: Robust Penalized Regression Estimator

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

Description

This set of penalized regression estimators offers the LASSO, MCP (minimax concave penalty), and SCAD (smoothly clipped absolute deviation) methods of regularization for robust Huber regression. These estimators are inspired by a series of papers by Wang et al (2018), Pan et al(2019), Sun et al (2019). The R package ILAMM has another implementation of these estimators. The optimal tuning parameter is selected based on a robust final prediction error (rfpe) metric.

Usage

robpr(
  formula,
  data,
  lambda = NULL,
  k = 1.345,
  gamma = NULL,
  penalty = c("LASSO", "MCP", "SCAD", "RIDGE")
)

Arguments

formula	model formula
data	a data frame
lambda	a lambda value. if left as NULL lambda will be estimated via optimization.
k	tuning constant for Huber's psi function. defaults to 1.345 which gives 95 pct efficiency when errors are normally distributed.
gamma	the tuning parameter for nonconvex penalties. If left as NULL, 3 is used for MCP and 3.7 is used for SCAD. Not applicable to LASSO.
penalty	one of "LASSO", "MCP", or "SCAD"

Value

a penreg object

References

Pan, X.O., Sun, Q., & Zhou, W. (2019). Nonconvex Regularized Robust Regression with Oracle Properties in Polynomial Time.
Sun, Q., Zhou, W-X. and Fan, J. (2019). Adaptive Huber regression. J. Amer. Stat. Assoc. 0 1-12.

Wang, L., Zheng, C., Zhou, W. and Zhou, W-X. (2018). A new principle for tuning-free Huber regression. Preprint.

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