The BerHu penalty and the grouped effect

Abstract

The Huber's criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. In the case of small sample size and large covariables numbers, this penalty is not very satisfactory variable selection method. In this paper, we introduce an adaptive reversed version of Huber's criterion as a penalty function. We call this penalty adaptive Berhu penalty. As for elastic net penalty, small coefficients contribute their ${\ell }_1$ norm to this penalty while larger coefficients cause it to grow quadratically (as ridge regression). We show that the estimator associated with criterion such that ordinary least square or Huber's one combining with adaptive Berhu penalty enjoys the oracle properties. In addition, this procedure encourages a grouping effect. This approach is compared with adaptive elastic net regularization. Extensive simulation studies demonstrate satisfactory finite-sample performance of such procedure. A real example is analyzed for illustration purposes. Keywords : Adaptive Berhu penalty; concomitant scale; elastic net penalty; Huber's criterion; oracle property; robust estimation.

38 pages, 10 figures

References in corpus (2)

• On the adaptive elastic-net with a diverging number of parameters
• The composite absolute penalties family for grouped and hierarchical variable selection

Cited by in corpus (8)

• Monocular Depth Estimation Based On Deep Learning: An Overview
• Learning Depth from Single Images with Deep Neural Network Embedding Focal Length
• BA-Net: Dense Bundle Adjustment Network
• On Deep Learning Techniques to Boost Monocular Depth Estimation for Autonomous Navigation
• Sparse-to-Continuous: Enhancing Monocular Depth Estimation using Occupancy Maps
• Attention-based Context Aggregation Network for Monocular Depth Estimation
• Recovering Homography from Camera Captured Documents using Convolutional Neural Networks
• Improving Monocular Depth Estimation by Leveraging Structural Awareness and Complementary Datasets