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Updated: May 9, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Robust Variable Selection with Exponential Squared Loss.

Xueqin Wang1, Yunlu Jiang, Mian Huang

  • 1Department of Statistical Science, School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China; and Zhongshan School of Medicine, Sun Yat-Sen University, Guangzhou, 510080, China; and Xinhua College, Sun Yat-Sen University, Guangzhou, 510520, China.

Journal of the American Statistical Association
|August 6, 2013
PubMed
Summary
This summary is machine-generated.

We introduce penalized robust regression estimators that offer robust variable selection and parameter estimation. Our method achieves the highest breakdown point, outperforming existing procedures in simulations and real-world data analysis.

Keywords:
Breakdown pointInfluence functionRobust regressionVariable selection

Related Experiment Videos

Last Updated: May 9, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Penalized regression is widely used for variable selection and robust estimation.
  • The robustness of existing penalized regression procedures is not well-characterized.
  • There is a need for robust methods that can handle influential points.

Purpose of the Study:

  • To propose a new class of penalized robust regression estimators.
  • To characterize the robustness of these new estimators.
  • To evaluate the performance of the proposed estimators against existing methods.

Main Methods:

  • Developing penalized robust regression estimators based on exponential squared loss.
  • Analyzing the theoretical properties, including oracle property and breakdown point.
  • Conducting simulation studies with influential points.
  • Re-analyzing benchmark datasets (Boston Housing, Plasma Beta-Carotene).

Main Results:

  • The proposed estimators are asymptotically normal and possess the oracle property.
  • Achieved the highest asymptotic breakdown point of 1/2 with bounded influence functions.
  • Simulation studies showed performance comparable to the oracle method, outperforming existing procedures.
  • Analysis of real datasets highlighted discrepancies with other penalized methods.

Conclusions:

  • The proposed penalized robust regression estimators offer superior robustness and performance.
  • These methods are crucial for reliable variable selection and estimation in the presence of outliers.
  • The findings underscore the importance of robust methods in regression analysis.