Abstract:
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In a high-dimensional linear regression model, a Gaussian error distribution has been frequently used because of its theoretical and computational conveniences. However, it may face some serious problems, such as overfitting and inaccurate uncertainty quantification, when the true error distribution is not a Gaussian distribution. We study asymptotic properties of a Bayesian linear regression model possibly with an unknown error distribution. A mixture prior distribution is adopted to fit the unknown error distribution, and properties of the posterior such as the convergence rate of the regression coefficient and the model selection consistency are studied under certain conditions.
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