Activity Number:
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62
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Type:
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Topic Contributed
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Date/Time:
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Sunday, July 31, 2016 : 4:00 PM to 5:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #320884
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Title:
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Bayesian High-Dimensional Sparse Models with Unknown Symmetric Errors
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Author(s):
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Lizhen Lin* and Minwoo Chae and David Dunson
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Companies:
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The University of Texas and The University of Texas at Austin and Duke University
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Keywords:
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Bayesian high-dimensional models ;
Unknown symmetric error ;
Sparse models ;
Semiparametric BVM
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Abstract:
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We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. Unknown error distribution is endowed with a symmetrized Dirichlet process mixture of normal prior. For the prior of regression coefficients, a mixture of point masses at zero and Laplace distributions is used. When the number of non-zero coefficients is of order $o(n^{-1/3})$ and the prior mass on it decreases exponentially, the marginal posterior distribution of regression coefficients is shown to contract at the optimal rate under compatibility conditions on the design matrix. The semiparametric Bernstein-von Mises theorem will be derived under stronger conditions.
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Authors who are presenting talks have a * after their name.