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Bayesian regression with nonparametric heteroskedasticity

Andriy Norets

Journal of Econometrics, 2015, vol. 185, issue 2, 409-419

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.

Keywords: Bayesian linear regression; Heteroskedasticity; Misspecification; Posterior consistency; Semiparametric Bernstein–von Mises theorem; Semiparametric efficiency; Gaussian process priors; Multivariate Bernstein polynomials (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (17)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:185:y:2015:i:2:p:409-419

DOI: 10.1016/j.jeconom.2014.12.006

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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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