Variable screening via quantile partial correlation.

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Ultra-high dimensional data presents challenges for traditional regression models.
• Variable selection is crucial for building accurate and interpretable quantile regression models.
• Identifying relevant predictors that influence conditional quantiles is complex, especially with weak marginal correlations.

Purpose of the Study:

• To develop a robust algorithm for variable screening and selection in ultra-high dimensional quantile linear regression.
• To address the challenge of selecting predictors that are important for conditional quantiles but not necessarily marginally correlated.
• To ensure theoretical guarantees for variable selection consistency and control the false selection rate.

Main Methods:

• Utilizing quantile partial correlation for an initial screening of candidate variables.
• Employing the extended Bayesian information criterion (EBIC) for optimal subset selection.
• Developing a two-stage approach combining screening and selection for enhanced predictor identification.

Main Results:

• The proposed algorithm achieves a 'sure screening set', identifying all relevant predictors.
• Theoretical analysis confirms model selection consistency by controlling the false selection rate.
• The method effectively handles highly correlated variables and identifies weakly correlated but important predictors.

Conclusions:

• The developed algorithm provides a reliable method for variable selection in ultra-high dimensional quantile regression.
• The practical application using EBIC ensures screening consistency.
• Simulation studies and an empirical example validate the algorithm's strong performance.