# Seminar

# Frequentist’s Properties of Posterior Distributions in Semiparametric Regression Models

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작성일Date

2017-09-28 17:53

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482

분야Field | Seminar | ||
---|---|---|---|

날짜Date | 2017-09-29 | 시간Time | 16:00 ~ 17:00 |

장소Place | Math. Bldg. 404 | 초청자Host | 포스텍수리응용센터 |

연사Speaker | Minwoo Chae | 소속Affiliation | Case Western Reserve university |

TOPIC | Frequentist’s Properties of Posterior Distributions in Semiparametric Regression Models | ||

소개 및 안내사항Content | In a smooth semiparametric model, the marginal posterior distribution for the ﬁ-nite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of any eﬃcient estimator. The assertion leads to asymptotic equiv-alence of credible and conﬁdence sets for the parameter of interest and is known as the semiparametric Bernstein-von Mises (sBvM) theorem. In this talk, the sBvM theorem is considered in regression models in which errors with symmetric densities play a role. Then, it is extended to a high-dimensional semiparametric model where most compo-nents of the regression coeﬃcient are zero. Various asymptotic properties such as optimal convergence rate, adaptation, distributional approximation and selection consistency are studied. The results guarantee asymptotic eﬃciency, adaptiveness to unknown sparsity level and error density, model selection consistency and valid uncertainty quantiﬁcation for Bayes procedures. |

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