Regression shrinkage and selection via least quantile shrinkage and selection operator.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Lasso and adaptive lasso are prominent variable selection techniques.
• Adaptive lasso assigns different penalties to coefficients but can increase bias with small initial coefficient values.
• Existing methods may not optimally handle high-dimensional data with complex coefficient structures.

Purpose of the Study:

• Introduce a novel weighted lasso method, the least quantile shrinkage and selection operator (lqsso).
• Address the bias issue in adaptive lasso by incorporating both signs and magnitudes of initial coefficients for weight determination.
• Evaluate the performance of lqsso, particularly in ultra-high-dimensional scenarios.

Main Methods:

• Developed the lqsso method, a new class of weighted lasso.
• The lqsso penalty incorporates information from the signs and magnitudes of initial coefficients.
• An efficient computational algorithm for lqsso was designed.
• Oracle properties of lqsso were demonstrated under mild conditions.

Main Results:

• Simulation studies show lqsso outperforms existing lasso methods in various aspects.
• The proposed method demonstrates particular superiority in ultra-high-dimensional settings.
• lqsso exhibits oracle properties, indicating its effectiveness in variable selection and coefficient estimation.

Conclusions:

• lqsso offers a robust alternative to existing lasso techniques, especially for high-dimensional data.
• The method effectively mitigates bias associated with adaptive lasso.
• The practical utility of lqsso is demonstrated through an application to a real-world dataset (rat eye).