中科院数学与系统科学研究院

科研进展与学术交流报告会

（第7期）

报告人一： 张新雨 研究员（系统科学研究所）

题 目 一：FROM MODEL SELECTION TO MODEL AVERAGING: A COMPARISON FOR NESTED LINEAR MODELS

摘 要 一: Model selection (MS) and model averaging (MA) are two popular approaches when having many candidate models. Theoretically, the estimation risk of an oracle MA is not larger than that of an oracle MS because the former one is more flexible, but a foundational issue is: does MA offer a substantial improvement over MS? Recently, a seminal work: Peng and Yang (2021), has answered this question under nested models with linear orthonormal series expansion. In the current paper, we further reply this question under linear nested regression models. Especially, a more general nested framework, heteroscedastic and autocorrelated random errors, and sparse coefficients are allowed in the current paper, which is more common in practice. In addition, we further compare MAs with different weight sets. Simulation studies support the theoretical findings in a variety of settings.(Jointly with Dr. Wenchao Xu).

报告人二： 朱天琪 副研究员（应用数学研究所）

题 目 二：最简单的物种树估计问题的复杂性

摘 要 二：多物种溯祖模型为解释基因树-物种树冲突提供了一个自然框架。目前已有多种基于多物种溯祖过程的物种树方法，但它们的统计特性仍然很难理解。在三个物种三条序列的情形下，我们估计了最常用几个物种树方法的可识别性、一致性和效率，并证明了物种树估计错误率分布的分位点与位点数量的平方根呈线性关系。我们的研究表明，即使在这种最简单的情况下，方法之间也存在重大差异。

时  间：2022.09.30(星期五), 10:40-13:00

地  点：数学院南楼N204室 / 腾讯会议310-238-170

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