Publication:
Bayesian Linear Regression with Conditional Heteroskedasticity

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URI: https://hdl.handle.net/10016/20436
ISSN: 2387-0303
UXXI: DT/0000001355
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ws1504.pdf (171.73 KB)
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2015-04-01
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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.
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Bayesian linear regression, Conditional heteroskedasticity, Rate of convergence, Posterior distribution, Adaptation, Hierarchical Gaussian spline prior, Log-spline prior
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DES - Working Papers. Statistics and Econometrics. WS