HIGH DIMENSIONAL VARIABLE SELECTION.

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• High-dimensional models present challenges for traditional statistical inference.
• Variable selection is crucial for model interpretability and performance in these settings.
• Existing methods may lack robust statistical guarantees.

Purpose of the Study:

• To provide statistical guarantees for variable selection in high-dimensional models.
• To evaluate the error rates and power of multi-stage regression methods.
• To introduce a novel screening and cleaning approach for variable selection.

Main Methods:

• A three-stage regression approach involving model screening, cross-validation, and hypothesis testing.
• Exploration of three screening methods: LASSO, marginal regression, and forward stepwise regression.
• Analysis of statistical properties like error rates and power.

Main Results:

• The proposed multi-stage method demonstrates consistent variable selection under certain theoretical conditions.
• Evaluation of the performance trade-offs between different screening techniques.
• Insights into the reliability of variable selection in high-dimensional contexts.

Conclusions:

• The developed multi-stage regression framework offers a principled way to achieve reliable variable selection.
• The findings contribute to understanding the statistical guarantees achievable in high-dimensional data analysis.
• This approach provides a valuable tool for researchers working with complex, high-dimensional datasets.