sqrtPENSEM: Square-Root Penalized Elastic Net MM-estimator

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

Description

This fits an penalized elastic net s-estimator with M-estimation step (making this an MM-estimator) using the square root method for selecting an optimal penalty parameter. No cross validation is required. Data are automatically unit scaled and centered using the Yohai and Zou τ location and scale estimate. Coefficients are returned on the original scale of the inputs. Hence, it is not neccessary to center and/or standardize the inputs here.

Usage

sqrtPENSEM(
  formula,
  data,
  alpha = 0.5,
  delta = 0.293,
  conf.level = 0.95,
  alg = c("lars", "dal")
)

Arguments

formula	a model formula
data	a data frame
alpha	a value between 0 and 1 for the mixing parameter. defaults to 0.5.
delta	the breakdown point for the robust estimator. the default is 0.293, somewhat arbitrarily (it is the breakdown point of the Theil-Sen estimator). the value must be greater than zero and at most 0.50.
conf.level	the confidence level to use in setting the penalty. the default is 0.95.
alg	should the augmented LARS ("lars") be used (the default), or should the Dual Augmented Lagrangian ("dal") option be used?

Value

a model fit

References

Belloni A.; Chernozhukov, V.; Wang, L. (2011) Square-root lasso: pivotal recovery of sparse signals via conic programming. Biometrika, 98(4):791-806.

Freue, G.V.C.; Kepplinger, D; Salibián-Barrera, M; Smucler, E. (2019) Robust elastic net estimators for variable selection and identification of proteomic biomarkers. Ann. Appl. Stat. 13(4):2065-2090. doi:10.1214/19-AOAS1269.

van de Geer S. (2016) The Square-Root Lasso. In: Estimation and Testing Under Sparsity. Lecture Notes in Mathematics, vol 2159. Springer, Cham

Raninen , E.; Ollila, E. (2017) Scaled and square-root elastic net. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, 2017, pp. 4336-4340. doi: 10.1109/ICASSP.2017.7952975

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