Heteroskedasticity-robust inference in Bayesian linear regression via the generalized method of moments

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Traditional Bayesian linear regression relies on assumptions like homoskedasticity and normality of error terms.
• Violations of these assumptions, particularly heteroskedasticity, can lead to inaccurate inference and poor coverage of credible intervals.

Purpose of the Study:

• To propose a semiparametric Bayesian approach for linear regression that does not require specifying error distribution.
• To develop a method robust to heteroskedasticity, providing valid inference and reliable uncertainty quantification.

Main Methods:

• Utilizes the Bayesian generalized method of moments (BGMM) for semiparametric Bayesian linear regression.
• Avoids distributional assumptions for the error term and the need for homoskedasticity.

Main Results:

• The proposed method provides accurate credible intervals with correct coverage, even under heteroskedasticity.
• Simulation studies demonstrate superior performance compared to frequentist and standard Bayesian methods under heteroskedasticity.
• Case studies confirm that ignoring heteroskedasticity can lead to misleading conclusions.

Conclusions:

• The semiparametric Bayesian approach using BGMM offers a robust and practical alternative to conventional likelihood-based methods.
• This method ensures reliable uncertainty quantification and valid statistical inference in the presence of heteroskedasticity.
• Potential for extensions to more complex linear models exists.