Drawing inferences for high-dimensional linear models: A selection-assisted partial regression and smoothing...

Area of Science:

• Statistics
• High-dimensional data analysis
• Genomic data analysis

Background:

• Inferences for high-dimensional models are complex due to inapplicable regular asymptotic theories.
• Existing methods may not adequately address simultaneous estimation and inference challenges.

Purpose of the Study:

• To propose a novel framework for simultaneous estimation and inference in high-dimensional linear models.
• To introduce the Selection-assisted Partial Regression and Smoothing (SPARES) procedure.

Main Methods:

• SPARES smooths partial regression estimates using variable selection to simplify to low-dimensional least squares.
• The method employs data splitting, variable selection, and partial regression.
• Asymptotic unbiasedness and normality are proven, with variance derived via a nonparametric delta method.

Main Results:

• The SPARES estimator is shown to be asymptotically unbiased and normal.
• Performance is evaluated through simulations and comparison with de-biased LASSO.
• The method successfully analyzed two genomic datasets, yielding biologically relevant findings.

Conclusions:

• SPARES provides a viable framework for simultaneous estimation and inference in high-dimensional linear models.
• The method offers a competitive alternative to existing techniques like de-biased LASSO.
• SPARES demonstrates practical utility in analyzing complex genomic data.