报告题目：Nonlinear Fréchet Regressions

报告人：林路 教授 （山东大学）

报告时间：2024年4月15日下午 15:00-16:00

报告地点：学院会议室109

报告摘要:

The existing Fréchet regression is actually defined within a linear framework, since the weight function in the Fréchet objective function is linearly defined, and the resulting Fréchet regression function is identified to be a linear model when the random object belongs to a Hilbert space. Even for nonparametric and semiparametric Fréchet regressions, which are usually nonlinear, the existing methods handle them by local linear (or local polynomial) technique, and the resulting Fréchet regressions are (locally) linear as well. We in this paper introduce a type of nonlinear Fréchet regressions. Such a framework can be utilized to fit the essentially nonlinear models in a general metric space and uniquely identify the nonlinear structure in a Hilbert space. Particularly, its generalized linear form can return to the standard linear Fréchet regression through a special choice of the weight function. Moreover, the generalized linear form possesses methodological and computational simplicity because the Euclidean variable and the metric space element are completely separable. The favorable theoretical properties (e.g. the estimation consistency and presentation theorem) of the nonlinear Fréchet regressions are established systemically. The comprehensive simulation studies and a human mortality data analysis demonstrate that the new strategy is significantly better than the competitors.

报告人简介：林路，山东大学中泰证券金融研究院教授、博士生导师，第一和第二届教育部应用统计专业硕士教育指导委员会成员，山东省教育厅应用统计专业硕士教育指导委员会成员，山东省政府参事，济南应用数学高等研究院院长。从事大数据、高维统计、非参数和半参数统计以及金融统计等方的研究，在国内外统计学、机器学习和相关应用学科顶级期刊和重要期刊(包括Ann. Statist., JMLR, Stat. Comput.和中国科学) 发表研究论文130余篇；多个金融策略资政报告得到省长的正面批示；主持过多项国家自然科学基金课题、全国统计科学研究重大项目、教育部博士点专项基金课题、教育部新文科课题、山东省自然科学基金重点项目等；获得国家统计局颁发的全国统计优秀研究成果一等和二等奖，山东省优秀教学成果一等奖(均排名第一)。