Bayesian Factor-adjusted Sparse Regression.

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Sparse regression methods often assume weak covariate correlation, which is frequently violated in economic and financial datasets.
• Strong correlations among covariates can hinder the performance of standard sparse regression techniques.

Purpose of the Study:

• To develop a novel sparse regression model that effectively handles strongly correlated covariates using a factor structure.
• To propose a semi-Bayesian estimation method for this factor-adjusted sparse regression model.

Main Methods:

• Modeling strongly correlated covariates via a factor structure, separating common factors and idiosyncratic components.
• Developing a semi-Bayesian approach for parameter estimation in the factor-adjusted sparse regression model.
• Employing non-asymptotic analyses to establish theoretical properties like estimation rate-optimality and model selection consistency.

Main Results:

• The proposed semi-Bayesian method demonstrates superior performance over the Lasso analogue in simulations.
• The method shows robustness to overestimating the number of common factors and minimal performance degradation with uncorrelated covariates.
• The approach scales effectively with increasing sample size, dimensionality, and sparsity, exhibiting fast convergence.

Conclusions:

• The factor-adjusted sparse regression model with a semi-Bayesian method provides a robust and efficient solution for analyzing economic and financial data with strongly correlated covariates.
• Empirical validation on U.S. bond risk premia and macroeconomic indicators supports the practical utility of the proposed method.