讲座题目：On efficient dimension reduction with respect to the interaction between two response variables

主 讲 人：浙江大学骆威研究员

讲座时间：2023年12月27日（周三）14：30 -15：30

讲座地点：6号学院楼402

主办单位：2138cn太阳集团古天乐、浙江省2011“数据科学与大数据分析协同创新中心”

摘要：

In this paper, we propose the novel theory and methodologies for dimension reduction with respect to the interaction between two response variables, which is a new research problem that has wide applications in missing data analysis, causal inference, and graphical models, etc. We formulate the parameters of interest to be the locally and the globally efficient dimension reduction subspaces, and justify the generality of the corresponding low-dimensional assumption. We then construct estimating equations that characterize these parameters, using which we develop a generic family of consistent, model-free, and easily implementable dimension reduction methods called the dual inverse regression methods. We also build the theory regarding the existence of the globally efficient dimension reduction subspace, and provide a handy way to check this in practice. The proposed work differs fundamentally from the literature of sufficient dimension reduction in terms of the research interest, the assumption adopted, the estimation methods, and the corresponding applications, and it potentially creates a new paradigm of dimension reduction research. Its usefulness is illustrated by simulation studies and a real data example at the end.

主讲人简介：

骆威，2014年毕业于美国宾夕法尼亚州立大学，之后任职于美国Baruch College,于2018年加入浙江大学。骆威的研究方向包括充分降维和因果推断，在Annals of Statistics, Biometrika, JRSSB等统计国际学术期刊上发表了多篇论文，目前主持国家优秀青年科学基金项目。

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