Factor-Adjusted Regularized Model Selection.

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• High-dimensional sparse regression models often face challenges with correlated covariates.
• Existing model selection methods struggle with cross-sectional and serial dependencies in data.
• Factor models offer a way to reduce covariate dependence in econometric and financial studies.

Purpose of the Study:

• To develop a consistent model selection strategy for high-dimensional sparse regression with dependent data.
• To address the limitations of current methods when dealing with highly correlated covariates.
• To propose a novel approach that handles both cross-sectional and serial dependencies.

Main Methods:

• Proposing Factor-Adjusted Regularized Model Selection (FarmSelect).
• Utilizing latent factors and idiosyncratic components as predictors.
• Transforming the problem from correlated to weakly correlated covariates via lifting.

Main Results:

• Achieving model selection consistency under mild conditions.
• Obtaining optimal rates of convergence.
• Demonstrating strong finite sample performance in model selection and prediction.
• Showing flexibility for weakly correlated and uncorrelated cases.

Conclusions:

• FarmSelect provides a robust solution for model selection in high-dimensional sparse regression with dependent data.
• The method effectively handles covariate dependence by leveraging factor models.
• FarmSelect is applicable to a broad range of problems and is available via an R-package.