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A Non-iterative Bayesian Sampling Algorithm for Linear Regression Models with Scale Mixtures of Normal Distributions

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Abstract

The scale mixtures of Normal distributions are used as a robust alternative to the normal distribution in linear regression modelling, and a non-iterative Bayesian sampling algorithm is developed to obtain independently and identically distributed samples approximately from the observed posterior distributions, which eliminates the convergence problems in iterative Gibbs sampling. Model selection and influential analysis are conducted to choose the best fitted model and to detect the latent outliers. The performances of the methodologies are illustrated through several simulation studies by comparison with the Normal regression and Gibbs sampling, and finally, the US treasury bond prices data is analyzed using the proposed algorithm.

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Acknowledgments

The authors gratefully acknowledge the editor and referees for their valuable comments and suggestions. This research is supported by The National Science Foundation of China Grants 11371227.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Fengkai Yang & Haijing Yuan

  2. School of Mathematics and Statistics, Shandong University, Weihai, 264209, China

    Fengkai Yang & Haijing Yuan

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  1. Fengkai Yang
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  2. Haijing Yuan
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Correspondence to Fengkai Yang.

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Yang, F., Yuan, H. A Non-iterative Bayesian Sampling Algorithm for Linear Regression Models with Scale Mixtures of Normal Distributions. Comput Econ 49, 579–597 (2017). https://doi.org/10.1007/s10614-016-9580-5

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  • DOI: https://doi.org/10.1007/s10614-016-9580-5

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