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Bayesian regression with nonparametric heteroskedasticity

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  • Norets, Andriy

Abstract

This paper studies large sample properties of a semiparametric Bayesian approach to inference in a linear regression model. The approach is to model the distribution of the regression error term by a normal distribution with the variance that is a flexible function of covariates. The main result of the paper is a semiparametric Bernstein–von Mises theorem under misspecification: even when the distribution of the regression error term is not normal, the posterior distribution of the properly recentered and rescaled regression coefficients converges to a normal distribution with the zero mean and the variance equal to the semiparametric efficiency bound.

Suggested Citation

  • Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    • Handle: RePEc:eee:econom:v:185:y:2015:i:2:p:409-419
    DOI: 10.1016/j.jeconom.2014.12.006
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    References listed on IDEAS

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    3. Zhao, Yanyun, 2015. "Bayesian Linear Regression with Conditional Heteroskedasticity," DES - Working Papers. Statistics and Econometrics. WS ws1504, Universidad Carlos III de Madrid. Departamento de Estadística.
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    8. Yuan Liao & Anna Simoni, 2016. "Bayesian Inference for Partially Identified Convex Models: Is it Valid for Frequentist Inference?," Departmental Working Papers 201607, Rutgers University, Department of Economics.
    9. Christoph Breunig & Ruixuan Liu & Zhengfei Yu, 2022. "Double Robust Bayesian Inference on Average Treatment Effects," Papers 2211.16298, arXiv.org, revised Feb 2024.
    10. Christopher D. Walker, 2023. "Parametrization, Prior Independence, and the Semiparametric Bernstein-von Mises Theorem for the Partially Linear Model," Papers 2306.03816, arXiv.org, revised Feb 2024.
    11. Lewis, Gabriel, 2022. "Heteroskedasticity and Clustered Covariances from a Bayesian Perspective," MPRA Paper 116662, University Library of Munich, Germany.

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