Two-stage subsampling variable selection for sparse high-dimensional generalized linear models.

Area of Science:

• High-dimensional data analysis
• Statistical modeling
• Bioinformatics

Background:

• Model selection in high-dimensional data, particularly omics data, remains a significant challenge.
• Existing methods offer room for improvement in accuracy and efficiency.

Purpose of the Study:

• To propose a novel two-stage subsampling approach for variable selection in high-dimensional generalized linear regression models.
• To enhance the accuracy and reliability of variable selection in complex datasets.

Main Methods:

• A two-stage subsampling strategy combining smoothly clipped absolute deviance (SCAD) penalty regularization and partial least squares (PLS) regression.
• Stage 1: Variable screening using SCAD and PLS on repeated subsamples.
• Stage 2: Refined variable selection using Akaike information criterion (AIC) on reduced predictor sets from Stage 1.

Main Results:

• The proposed method demonstrates superior performance compared to existing approaches in simulation studies.
• Achieved high probability of selecting the true model with a low number of false positives.
• Proven $n^{1/2}$-consistency for the first-stage estimator.

Conclusions:

• The two-stage subsampling approach offers a robust and effective solution for variable selection in high-dimensional settings.
• The method is applicable to various regression models including logistic, Poisson, and linear regression.
• Successfully illustrated on gene expression cancer datasets, highlighting its practical utility.