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Bayesian Linear Regression with Conditional Heteroskedasticity

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  • Zhao, Yanyun

Abstract

In this paper we consider adaptive Bayesian semiparametric analysis of the linear regression model in the presence of conditional heteroskedasticity. The distribution of the error term on predictors are modelled by a normal distribution with covariate-dependent variance. We show that a rate-adaptive procedure for all smoothness levels of this standard deviation function is performed if the prior is properly chosen. More specifically, we derive adaptive posterior distribution rate up to a logarithm factor for the conditional standard deviation based on a transformation of hierarchical Gaussian spline prior and log-spline prior respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:cte:wsrepe:ws1504
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    References listed on IDEAS

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    1. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    2. Norets, Andriy & Pati, Debdeep, 2017. "Adaptive Bayesian Estimation Of Conditional Densities," Econometric Theory, Cambridge University Press, vol. 33(4), pages 980-1012, August.
    3. Pelenis, Justinas, 2014. "Bayesian regression with heteroscedastic error density and parametric mean function," Journal of Econometrics, Elsevier, vol. 178(P3), pages 624-638.
    4. repec:dau:papers:123456789/3984 is not listed on IDEAS
    5. Lizhen Lin & David B. Dunson, 2014. "Bayesian monotone regression using Gaussian process projection," Biometrika, Biometrika Trust, vol. 101(2), pages 303-317.
    6. Weining Shen & Surya T. Tokdar & Subhashis Ghosal, 2013. "Adaptive Bayesian multivariate density estimation with Dirichlet mixtures," Biometrika, Biometrika Trust, vol. 100(3), pages 623-640.
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    Cited by:

    1. Lewis, Gabriel, 2022. "Heteroskedasticity and Clustered Covariances from a Bayesian Perspective," MPRA Paper 116662, University Library of Munich, Germany.

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    Bayesian linear regression;

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