Efficient test-based variable selection for high-dimensional linear models.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Variable selection is crucial in high-dimensional data analysis.
• Existing methods like Forward Stepwise Regression (FSR) and Least Angle Regression (LARS) often rely on cross-validation (CV) for stopping criteria.
• Cross-validation (CV) suffers from high computational costs and lacks statistical interpretation.

Purpose of the Study:

• To introduce a novel, flexible, and efficient test-based variable selection approach.
• To overcome the limitations of computational expense and lack of statistical interpretation associated with cross-validation (CV).
• To develop a stopping criterion for sequential variable selection procedures in high-dimensional settings.

Main Methods:

• A new test is proposed based on maximal absolute partial correlation between inactive and response variables, conditional on active variables.
• The asymptotic null distribution of the test statistic is derived for high dimensions.
• The test is shown to be consistent, with variables added based on a pre-defined p-value threshold.

Main Results:

• The proposed test-based method is incorporated into sequential selection procedures.
• Numerical studies demonstrate competitive performance compared to cross-validation (CV).
• The method shows strong variable selection accuracy and reduced computational complexity.

Conclusions:

• The introduced test-based variable selection approach provides a viable and efficient alternative to cross-validation (CV).
• This method enhances statistical interpretability while maintaining high performance in variable selection.
• It offers a promising solution for analyzing high-dimensional data effectively.