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Related Experiment Video

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An Operant Intra-/Extra-dimensional Set-shift Task for Mice

An Operant Intra-/Extra-dimensional Set-shift Task for Mice

Published on: January 22, 2016

Penalized and constrained LAD estimation in fixed and high dimension.

Xiaofei Wu¹, Rongmei Liang¹, Hu Yang¹

¹College of Mathematics and Statistics, Chongqing University, Chongqing, 401331 People's Republic of China.

Statistical Papers (Berlin, Germany)

|April 5, 2021

Summary

This study introduces a penalized LAD estimation method incorporating linear constraints, offering improved performance with heavy-tailed errors and outliers. The new method demonstrates theoretical advantages in both fixed and high-dimensional settings, outperforming existing techniques.

Keywords:

ADMM High dimensional regression LADLasso Linear constraints Oracle property Variable selection

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Area of Science:

Statistics
Econometrics
Machine Learning

Background:

Prior information and structure in applications can be modeled as constraints on regression coefficients.
Existing methods like constrained lasso may not perform optimally with heavy-tailed errors or outliers.

Purpose of the Study:

To propose a novel penalized LAD (Least Absolute Deviations) estimation incorporating linear constraints.
To address limitations of existing methods in the presence of heavy-tailed errors and outliers.

Main Methods:

Developed a penalized LAD estimation with linear constraints.
Utilized linear programming for fixed-dimension coefficient estimation.
Implemented a nested alternating direction method of multipliers (ADMM) for high-dimensional settings.

Main Results:

The proposed estimation exhibits the Oracle property with adjusted normal variance in fixed dimensions.
In high-dimensional cases (p >> n), the error bound is sharper than existing methods.
The method is robust across various noise distributions, including the Cauchy distribution.

Conclusions:

The penalized LAD estimation with linear constraints is a robust and effective alternative, especially when constrained lasso methods are unreliable.
Theoretical and simulation results validate the proposed method's performance in diverse statistical scenarios.